All Preprints

2009 Preprints

• 2009-055 Tore Flåtten, Alexandre Morin and Svend Tollak Munkejord:
  Wave propagation in multicomponent flow models.
• 2009-054 Rinaldo M. Colombo, Graziano Guerra and Francesca Monti:
  Modeling the Dynamics of Granular Matter.
• 2009-053 Kenneth Karlsen and Trygve Karper:
  A convergent mixed method for the Stokes approximation of viscous compressible flow.
• 2009-052 Helge Holden and Xavier Raynaud:
  Global semigroup of conservative solutions of the nonlinear variational wave equation.
• 2009-051 Helge Holden, Kenneth H. Karlsen, Darko Mitrovic and Evgueni Yu. Panov:
  Strong compactness of approximate solutions to degenerate elliptic-hyperbolic equations with discontinuous flux function.
• 2009-050 Frederike Kissling and Christian Rohde:
  The computation of nonclassical shock waves with a heterogeneous multiscale method.
• 2009-049 Patrick Engel and Christian Rohde:
  Convergence of the space-time expansion discontinuous Galerkin method for scalar conservation laws.
• 2009-048 Nathaël Alibaud and Boris Andreïanov:
  Non-uniqueness of weak solutions for the fractal Burgers equation.
• 2009-047 Boris Andreianov and Mohamed Maliki:
  A note on uniqueness of entropy solutions to degenerate parabolic equations in R^N.
• 2009-046 Zhen-huan Teng:
  Error bound between monotone difference schemes and their modified equations.
• 2009-045 Darko Mitrovic and Jelena Aleksić:
  On the compactness for two dimensional scalar conservation law with discontinuous flux.
• 2009-044 Jiale Hua and Tong Yang:
  A note on the new Glimm functional for general systems of hyperbolic conservation laws.
• 2009-043 Yingjie Liu, Chi-Wang Shu and Zhiliang Xu:
  Hierarchical reconstruction with up to second degree remainder for solving nonlinear conservation laws.
• 2009-042 Stefano Bianchini and Laura V. Spinolo:
  Invariant manifolds for a singular ordinary differential equation.
• 2009-041 Stefano Bianchini and Laura V. Spinolo:
  A connection between viscous profiles and singular ODEs.
• 2009-040 Qibing Li and Kun Xu:
  A high-order gas-kinetic navier-stokes solver I: One-dimensional flux evaluation.
• 2009-039 Nikolay Andrianov:
  On an optimal number of time steps for a sequential solution of an elliptic–hyperbolic system.
• 2009-038 Helge Holden, Kenneth H. Karlsen, Nils Henrik Risebro and Terence Tao:
  Operator splitting for the KdV equation.
• 2009-037 Harald Hanche-Olsen and Helge Holden:
  The Kolmogorov–Riesz compactness theorem.
• 2009-036 Helge Kristian Jenssen and Trygve K. Karper:
  1D compressible flow with temperature dependent transport coefficients.
• 2009-035 Kenneth H. Karlsen and Trygve K. Karper:
  A convergent nonconforming finite element method for compressible Stokes flow.
• 2009-034 Alain-Yves LeRoux:
  The linear appearance theorem for a class of non linear non homogeneous hyperbolic systems involving a transport equation.
• 2009-033 François Bouchut and Vladimir Zeitlin:
  A robust well-balanced scheme for multi-layer shallow water equations.
• 2009-032 François Bouchut and Tomás Morales de Luna:
  A subsonic-well-balanced reconstruction scheme for shallow water flows.
• 2009-031 Jishan Fan, Song Jiang and Yaobin Ou:
  A blow-up criterion for compressible viscous heat-conductive flows.
• 2009-030 I. H. Biswas, E. R. Jakobsen and K. H. Karlsen:
  Difference-quadrature schemes for nonlinear degenerate parabolic integro-PDE.
• 2009-029 Simone Cifani, Espen R. Jakobsen and Kenneth H. Karlsen:
  The discontinuous Galerkin method for fractal conservation laws.
• 2009-028 João Paulo Dias, Mario Figueira and Hermano Frid:
  Vanishing viscosity with short wave long wave interactions for systems of conservation laws.
• 2009-027 Darko Mitrovic:
  Existence and Uniqueness for Multidimensional Scalar Conservation Law with Discontinuous Flux.
• 2009-026 Hermano Frid and Jean C. Silva:
  Homogenization of Nonlinear PDE's in the Fourier–Stieltjes Algebras.
• 2009-025 Juhi Jang and Ning Jiang:
  Acoustic limit of the Boltzmann equation: Classical solutions.
• 2009-024 Ning Jiang, C. David Levermore and Nader Masmoudi:
  Remarks on the acoustic limit for the Boltzmann equation.
• 2009-023 Ning Jiang and C. David Levermore:
  Weakly Nonlinear-Dissipative Approximations of Hyperbolic-Parabolic Systems with Entropy.
• 2009-022 Alberto Bressan, Helge Holden and Xavier Raynaud:
  Lipschitz metric for the Hunter–Saxton equation.
• 2009-021 Helge Kristian Jenssen and Irina Kogan:
  Systems of hyperbolic conservation laws with prescribed eigencurves.
• 2009-020 Stéphane Junca and Bruno Lombard:
  Dilatation of a one-dimensional nonlinear crack impacted by a periodic elastic wave.
• 2009-019 E.Yu. Panov:
  Ultra-parabolic equations with rough coefficients. Entropy solutions and strong pre-compactness property.
• 2009-018 Erik Endres, Helge Kristian Jenssen and Mark Williams:
  Singularly perturbed ODEs and profiles for stationary symmetric Euler and Navier–Stokes shocks.
• 2009-017 Guy Vallet and Petra Wittbold:
  On a stochastic first order hyperbolic equation in a bounded domain.
• 2009-016 Kenneth H. Karlsen and Trygve K. Karper:
  Convergence of a mixed method for a semi-stationary compressible Stokes system.
• 2009-015 Luigi Ambrosio, Gianluca Crippa, Alessio Figalli and Laura V. Spinolo:
  Some new well-posedness results for continuity and transport equations, and applications to the chromatography system.
• 2009-014 Helge Holden, Kenneth H. Karlsen and Darko Mitrovic:
  Zero diffusion-dispersion-smoothing limits for scalar conservation law with discontinuous flux function.
• 2009-013 Darko Mitrovic:
  New entropy conditions for the scalar conservation law with discontinuous flux.
• 2009-012 F. Ancona and A. Marson:
  Sharp convergence rate of the Glimm scheme for general nonlinear hyperbolic systems.
• 2009-010 Boris Andreianov, Paola Goatin and Nicolas Seguin:
  Finite volume schemes for locally constrained conservation laws.
• 2009-009 Kun Xu and Zhaoli Guo:
  Extended Gas Dynamic Equations for Microflows.
• 2009-008 Zhi-Qiang Shao:
  Asymptotic behavior of global classical solutions to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small BV data.
• 2009-007 Kenneth H. Karlsen and Suleyman Ulusoy:
  Stability of entropy solutions for Lévy mixed hyperbolic-parabolic equations.
• 2009-006 D. Donatelli and P. Marcati:
  Leray weak solutions of the Incompressible Navier Stokes system on exterior domains via the artificial compressibility method.
• 2009-005 Naoki Tsuge:
  Large time decay of solutions to isentropic gas dynamics with spherical symmetry.
• 2009-004 Marek Brandner, Jiří Egermaier and Hana Kopincová:
  Numerical methods for river flow modelling.
• 2009-003 Debora Amadori and Wen Shen:
  The Slow Erosion Limit in a Model of Granular Flow.
• 2009-002 David H. Wagner:
  Symmetric Hyperbolic Equations of Motion for a Hyperelastic Material.
• 2009-001 Boris Andreianov, Mostafa Bendahmane and Kenneth H. Karlsen:
  Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations.

2008 Preprints

• 2008-041 Jinghua Wang:
  Regularity of entropy solutions.
• 2008-040 Knut Waagan:
  A positive MUSCL–Hancock scheme for ideal magnetohydrodynamics.
• 2008-039 Kenneth H. Karlsen and Trygve K. Karper:
  Convergent finite element methods for compressible barotropic Stokes systems.
• 2008-038 Helge Holden, Nils Henrik Risebro and Hilde Sande:
  Front tracking for a model of immiscible gas flow with large data.
• 2008-037 Naoki Tsuge:
  Global L^∞ solutions of the compressible Euler Equations with spherical symmetry.
• 2008-036 G. M. Coclite, K. H. Karlsen and Y.-S. Kwon:
  Initial-boundary value problems for conservation laws with source terms and the Degasperis–Procesi equation.
• 2008-035 Blake Temple and Robin Young:
  A Liapunov-Schmidt Reduction for Time-Periodic Solutions of the Compressible Euler Equations.
• 2008-034 Blake Temple and Robin Young:
  Time-Periodic Linearized Solutions of the Compressible Euler Equations and a Problem of Small Divisors.
• 2008-033 Blake Temple and Robin Young:
  A Paradigm for Time-Periodic Sound Wave Propagation in the Compressible Euler Equations.
• 2008-032 Robin Young:
  Global Wave Interactions in Isentropic Gas Dynamics.
• 2008-031 Boris Andreianov, Mostafa Bendahmane, Kenneth H. Karlsen and Stanislas Ouaro:
  Well-posedness results for triply nonlinear degenerate parabolic equations.
• 2008-030 Tao Tang, Jinghua Wang and Yinchuan Zhao:
  Regularity and Global Structure of Solutions to Hamilton–Jacobi equations II. Convex initial data.
• 2008-029 K. R. Arun and Phoolan Prasad:
  3-D kinematical Conservation Laws: Equations of Evolution of a Surface.
• 2008-028 S. Jaisankar and S.V. Raghurama:
  A Central Rankine Hugoniot Solver for Hyperbolic Conservation Laws.
• 2008-027 Darko Mitrović:
  On a strong precompactness of velocity averages for a heterogenous transport equation with rough coefficients.
• 2008-026 K.R. Arun, M. Kraft and M. Lukáčová-Medviďová:
  Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions.
• 2008-025 K.R. Arun, M. Lukáčová-Medviďová, S.V. Raghurama and Phoolan Prasad:
  An application of 3-D kinematical conservation laws: Propagation of a three dimensional wavefront.
• 2008-024 Yossi Farjoun and Benjamin Seibold:
  An exactly conservative particle method for one dimensional scalar conservation laws.
• 2008-023 Debora Amadori and Wen Shen:
  Global Existence of Large BV Solutions in a Model of Granular Flow.
• 2008-022 E.Yu. Panov:
  On the strong pre-compactness property for entropy solutions of an ultra-parabolic equation with discontinuous flux.
• 2008-021 Misha Perepelitsa:
  Asymptotics toward rarefaction waves and vacuum for 1-d Compressible Navier–Stokes equations.
• 2008-020 Jan Giesselmann:
  A convergence result for finite volume schemes on 2-dimensional Riemannian manifolds.
• 2008-019 Alain-Yves LeRoux:
  A mathematical model for tsunami generation using a conservative velocity-pressure hyperbolic system.
• 2008-018 François Bouchut, Christian Klingenberg and Knut Waagan:
  A multiwave approximate Riemann solver for ideal MHD based on relaxation II – Numerical implementation with 3 and 5 waves.
• 2008-017 E.Yu. Panov:
  On weak convergence of entropy solutions to scalar conservation laws.
• 2008-016 E.Yu. Panov:
  On existence and uniqueness of entropy solutions to the Cauchy problem for a conservation law with discontinuous flux.
• 2008-015 Jiale Hua, Zaihong Jiang and Tong Yang:
  A New Glimm Functional and Convergence Rate of Glimm Scheme for General Systems of Hyperbolic Conservation Laws.
• 2008-014 Erik Endres and Helge Kristian Jenssen:
  Compressible 1-D Euler Equations with Large Data: A Case Study.
• 2008-013 Erik Endres, Helge Kristian Jenssen and Mark Williams:
  Symmetric Euler and Navier–Stokes shocks in stationary barotropic flow on a bounded domain.
• 2008-012 Helge Holden and Xavier Raynaud:
  Dissipative solutions for the Camassa–Holm equation.
• 2008-011 Darko Mitrovic, Vladimir Danilov, Velibor Bojkovic:
  Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process.
• 2008-010 Alain-Yves LeRoux:
  Sound traveling-waves in wind instruments as solutions to non linear non homogeneous gas dynamics equations.
• 2008-009 Yong-Jung Kim and Young-Ran Lee:
  Structure of fundamental solutions of a conservation law without convexity.
• 2008-008 Corrado Mascia and Kevin Zumbrun:
  Spectral stability of weak relaxation shock profiles.
• 2008-007 Misha Perepelitsa:
  Dynamics of the density discontinuity interface. A transversal contact problem.
• 2008-006 Giuseppe Maria Coclite, Kenneth H. Karlsen and Nils Henrik Risebro:
  An explicit finite difference scheme for the Camassa–Holm equation.
• 2008-005 Marte Godvik and Harald Hanche-Olsen:
  Car-following and the macroscopic Aw–Rascle traffic flow model.
• 2008-004 Michaël Baudin, Frédéric Coquel and Quang Huy Tran:
  A relaxation method via the Born–Infeld system.
• 2008-003 Quang Huy Tran:
  Second-order slope limiters for the simultaneous linear advection of (not so) independent variables.
• 2008-002 Yossi Farjoun and Benjamin Seibold:
  Solving one dimensional scalar conservation laws by particle management.
• 2008-001 Stefan Diehl:
  A uniqueness condition for non-linear convection-diffusion equations with discontinuous coefficients.

2007 Preprints

• 2007-032 V.M. Shelkovich:
  Singular solutions to systems of conservation laws: shocks, δ- and δ'-shocks.
• 2007-031 V.M. Shelkovich:
  Multidimensional delta-shocks and the transportation and concentration processes.
• 2007-030 Camillo De Lellis and László Székelyhidi:
  On admissibility criteria for weak solutions of the Euler equation.
• 2007-029 F. G. Fuchs, K. H. Karlsen, S. Mishra and N. H. Risebro:
  Stable upwind schemes for the magnetic induction equation.
• 2007-028 E.Yu. Panov:
  On the Dirichlet problem for first order quasilinear equations on a manifold.
• 2007-027 Helge Holden, Nils Henrik Risebro and Hilde Sande:
  The solution of the Cauchy problem with large data for a model of a mixture of gases.
• 2007-026 Gui-Qiang Chen, Nadine Even and Christan Klingenberg:
  Hyperbolic Conservation Laws with Discontinuous Fluxes and Hydrodynamic Limit for Particle Systems.
• 2007-025 Steinar Evje and Kenneth H. Karlsen:
  Global existence of weak solutions for a viscous two-phase model.
• 2007-024 Jun Chen:
  Subsonic Flows for the Full Euler Equations in Half Plane.
• 2007-023 Rinaldo M. Colombo and Mauro Garavello:
  Phase Transition Model for Traffic at a Junction.
• 2007-022 Yong-Jung Kim and Youngsoo Ha:
  Fundamental solutions of conservation laws.
• 2007-021 Thomas Curtright and David Fairlie:
  Euler Incognito.
• 2007-020 Christian Rohde and Wen-An Yong:
  Dissipative Entropy and Global Smooth Solutions for Radiation Hydrodynamics and Magnetohydrodynamics.
• 2007-019 Alberto Bressan and Carlotta Donadello:
  On the Convergence of Viscous Approximations After Shock Interactions.
• 2007-018 Raimund Bürger, Antonio García, Kenneth H. Karlsen and John D. Towers:
  Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model.
• 2007-017 Mikio Akamatsu, Katsuhiro Watanabe and Toshiyuki Arima:
  Mach-uniform accuracy and efficiency of a semi-implicit/explicit algorithm to solve compressible Euler equations for general fluids.
• 2007-016 H. Holden, K. H. Karlsen and N. H. Risebro:
  A convergent finite difference method for a nonlinear variational wave equation.
• 2007-015 Alexander Dressel and Christian Rohde:
  Time-asymptotic behaviour of weak solutions for a viscoelastic two-phase model with nonlocal capillarity.
• 2007-014 Eitan Tadmor and Weigang Zhong:
  Energy-preserving and stable approximations for the two-dimensional shallow water equations.
• 2007-013 Roger Robyr:
  SBV regularity of entropy solutions for a class of genuinely nonlinear scalar balance laws with non-convex flux function.
• 2007-012 Bin Cheng and Eitan Tadmor:
  Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations.
• 2007-011 Raimund Bürger, Kenneth H. Karlsen and John D. Towers:
  An Engquist–Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections.
• 2007-010 Alexander Dressel and Christian Rohde:
  Global existence and uniqueness of solutions for a viscoelastic two-phase model with nonlocal capillarity.
• 2007-009 E.Yu. Panov:
  Existence and strong pre-compactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux.
• 2007-008 Gunilla Kreiss, Heinz-Otto Kreiss and Jens Lorenz:
  Stability of Viscous Shocks on Finite Intervalls.
• 2007-007 Sebastian Noelle, Yulong Xing, and Chi-Wang Shu:
  High Order Well-balanced Finite Volume WENO Schemes for Shallow Water Equation with Moving Water.
• 2007-006 Xiao-Biao Lin:
  Gearhart–Prüss Theorem and linear stability for Riemann solutions of conservation laws.
• 2007-005 T. Li and H. Liu:
  Critical thresholds in a relaxation model for travel flows.
• 2007-004 H. Liu and Z.M. Wang:
  A Field Space-based Level set Method for Computing Multi-valued Solutions.
• 2007-003 Kenneth Hvistendahl Karlsen, Michel Rascle and Eitan Tadmor:
  On the existence and compactness of a two-dimensional resonant system of conservation laws.
• 2007-002 Misha Perepelitsa:
  The Navier–Stokes equations for the motion of compressible, viscous fluid flows with the no-slip boundary condition.
• 2007-001 Marte Godvik and Harald Hanche-Olsen:
  Existence of solutions for the Aw–Rascle traffic flow model with vacuum.

2006 Preprints

• 2006-058 Misha Perepelitsa:
  A Model Problem for the Motion of a Compressible, Viscous Fluid Flow with the No-Slip Boundary Condition.
• 2006-057 V.G. Danilov and D. Mitrovic:
  Delta shock wave formation in the case of triangular hyperbolic system of conservation laws.
• 2006-056 S. Albeverio and V.M. Shelkovich:
  On the Delta-Shock Front Problem.
• 2006-055 Christian Klingenberg, Wolfram Schmidt and Knut Waagan:
  Numerical comparison of Riemann solvers for astrophysical hydrodynamics.
• 2006-054 Wen Shen:
  On the Shape of Avalanches.
• 2006-053 V.M. Shelkovich:
  On delta-shocks and singular shocks.
• 2006-052 Christophe Chalons and Paola Goatin:
  Godunov scheme and sampling technique for computing phase transitions in traffic flow modeling.
• 2006-051 Christophe Chalons:
  Transport-Equilibrium Schemes for Computing Nonclassical Shocks. Scalar Conservation Laws.
• 2006-050 Katja Baumbach and Maria Lukáčová-Medviďová:
  On the Comparison of Evolution Galerkin and Discontinuous Galerkin Schemes.
• 2006-049 Wen Shen and Zhengfu Xu:
  Vanishing Viscosity Approximation to Hyperbolic Conservation Laws.
• 2006-048 Knut Waagan:
  Convergence rate of monotone numerical schemes for Hamilton-Jacobi equations with weak boundary conditions.
• 2006-047 Cleopatra Christoforou:
  Systems of Hyperbolic Conservation Laws with Memory.
• 2006-046 Kenneth H. Karlsen, Siddhartha Mishra and Nils Henrik Risebro:
  Well-Balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation.
• 2006-045 E. Yu. Panov:
  Existence of strong traces for quasi-solutions of multidimensional scalar conservation laws.
• 2006-044 Jiequan Li and Yuxi Zheng:
  Interaction of Rarefaction Waves of the Two-Dimensional Self-Similar Euler Equations.
• 2006-043 F. Bouchut, C. Klingenberg, and K. Waagan:
  A multiwave approximate Riemann solver for ideal MHD based on relaxation I – Theoretical framework.
• 2006-042 S. Sazhenkov:
  Effective Thermoviscoelasticity of a Saturated Porous Ground.
• 2006-041 V. G. Danilov:
  On singularities of conservation equation solution. (Updated 2006-11-10.)
• 2006-040 Raimund Bürger, Antonio García, Kenneth H. Karlsen and John D. Towers:
  A family of schemes for kinematic flows with discontinuous flux.
• 2006-039 Yingjie Liu, Chi-Wang Shu, Eitan Tadmor, and Mengping Zhang:
  Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes.
• 2006-038 Giuseppe Maria Coclite, Kenneth Hvistendahl Karlsen and Nils Henrik Risebro:
  A convergent finite difference scheme for the Camassa–Holm equation with general H¹ initial data.
• 2006-035 Helge Holden and Xavier Raynaud:
  Periodic conservative solutions of the Camassa–Holm equation.
• 2006-034 Yann Brenier:
  L² formulation of multidimensional scalar conservation laws.
• 2006-033 V. G. Danilov:
  Remarks on vacuum state and uniqueness of concentration process.
• 2006-032 Eitan Tadmor and Dongming Wei:
  On the global regularity of sub-critical Euler–Poisson equations with pressure.
• 2006-031 T. Tang, J.-H. Wang and Y.-C. Zhao:
  On the piecewise smoothness of entropy solutions to scalar conservation laws for a large class of initial data.
• 2006-030 Song Jiang and Wenjun Sun:
  A second-order BGK scheme for the equations of radiation hydrodynamics.
• 2006-029 Yingjie Liu, Chi-Wang Shu, Eitan Tadmor, and Mengping Zhang:
  Central Discontinuous Galerkin Methods on Overlapping Cells with a Non-Oscillatory Hierarchical Reconstruction.
• 2006-028 Donatella Donatelli and Pierangelo Marcati:
  A dispersive approach to the artificial compressibility approximations of the Navier Stokes equations in 3-D.
• 2006-027 Gui-Qiang Chen, Cleopatra Christoforou and Yongqian Zhang:
  Dependence of Entropy Solutions in the Large for the Euler Equations on Nonlinear Flux Functions.
• 2006-026 Matania Ben-Artzi and Jiequan Li:
  Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem.
• 2006-025 Gui-Qiang Chen, Constantine Dafermos, Marshall Slemrod, and Dehua Wang:
  On Two-Dimensional Sonic-Subsonic Flow.
• 2006-024 Xiao-Biao Lin:
  Slow eigenvalues of self-similar solutions of the Dafermos regularization of a system of conservation laws: An analytic approach.
• 2006-023 Alberto Bressan and Adrian Constantin:
  Global Dissipative Solutions of the Camassa–Holm Equation.
• 2006-022 Alberto Bressan and Wen Shen:
  Optimality Conditions for Solutions to Hyperbolic Balance Laws.
• 2006-021 Stefano Bianchini and Laura V. Spinolo:
  The boundary Riemann solver coming from the real vanishing viscosity approximation.
• 2006-020 Xiao-Biao Lin:
  Analytic Semigroup Generated by the Linearization of a Riemann–Dafermos Solution.
• 2006-019 Xiao-Biao Lin:
  L² semigroup and linear stability for Riemann solutions of conservation laws.
• 2006-018 Helge Holden and Xavier Raynaud:
  Global conservative solutions of the generalized hyperelastic-rod wave equation.
• 2006-017 Kenneth H. Karlsen, Siddhartha Mishra and Nils Henrik Risebro:
  Convergence of finite volume schemes for triangular systems of conservation laws.
• 2006-016 Cleopatra Christoforou:
  Uniqueness and Sharp Estimates on Solutions to Hyperbolic Systems with Dissipative Source.
• 2006-015 Gui-Qiang Chen and Cleopatra Christoforou:
  Solutions for a Nonlocal Conservation Law with Fading Memory.
• 2006-014 Gui-Qiang Chen and Mikhail Feldman:
  Global Solutions of Shock Reflection by Large-Angle Wedges for Potential Flow.
• 2006-013 Giuseppe Maria Coclite, Kenneth Hvistendahl Karlsen and Nils Henrik Risebro:
  Numerical schemes for computing discontinuous solutions of the Degasperis–Procesi equation.
• 2006-012 Xinhua Zhong and Song Jiang:
  Local existence and finite-time blow-up in multidimensional radiation hydrodynamics.
• 2006-011 Helge Holden and Xavier Raynaud:
  Global conservative multipeakon solutions of the Camassa-Holm equation.
• 2006-010 Shi Jin and Xiaomei Liao:
  A Hamiltonian-preserving scheme for high frequency elastic waves in heterogeneous media.
• 2006-009 N. Costanzino, H. K. Jenssen, G. Lyng, and M. Williams:
  Existence and stability of curved multidimensional detonation fronts.
• 2006-008 Kristen DeVault, Pierre Gremaud, and Helge Kristian Jenssen:
  Numerical investigation of cavitation in multi-dimensional compressible flows.
• 2006-007 Chunjin Lin, Jean-Francois Coulombel, and Thierry Goudon:
  Shock profiles for non-equilibrium radiating gases.
• 2006-006 Song Jiang, Guoxi Ni, and Wenjun Sun:
  Vanishing viscosity limit to rarefaction waves for the Navier-Stokes equations of one-dimensional compressible heat-conducting fluids.
• 2006-005 Francois Bouchut and Gianluca Crippa:
  On the relations between uniqueness for the Cauchy problem and existence of smooth approximations for linear transport equations.
• 2006-004 Giuseppe Maria Coclite and Kenneth Hvistendahl Karlsen:
  On the uniqueness of discontinuous solutions to the Degasperis-Procesi equation.
• 2006-003 J. A. Carrillo, M. Di Francesco, and C. Lattanzio:
  Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws.
• 2006-002 Peng Zhang:
  Characteristic parameters of a wide cluster in a higher-order traffic flow.
• 2006-001 Helge Holden and Xavier Raynaud:
  Global conservative solutions of the Camassa-Holm equation - a Lagrangian point of view.

2005 Preprints

• 2005-055 A. Yu. Khrennikov and V. M. Shelkovich:
  On the algebraic aspect of singular solutions to conservation laws systems.
• 2005-054 Wen Chen:
  Fractional and fractal derivatives modeling of turbulence.
• 2005-053 V. M. Shelkovich:
  The Riemann problem admitting δ′-shock wave type solution (the vanishing viscosity approach).
• 2005-052 Paola Goatin:
  The Aw–Rascle traffic flow model with phase transitions.
• 2005-051 E.Yu. Panov:
  On symmetrizability of hyperbolic matrix spaces.
• 2005-050 E.Yu. Panov:
  Prolonged systems for a scalar conservation law and entropies of higher order.
• 2005-049 E.Yu. Panov:
  On infinite dimensional systems of conservation laws of Keyfitz-Kranzer type.
• 2005-048 A.-Y. LeRoux and M.-N. LeRoux:
  A Mathematical model for rogue waves, using Saint Venant equations with friction.
• 2005-047 S. Bianchini, B. Hanouzet, and R. Natalini:
  Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy.
• 2005-046 Jorge Balbas and Eitan Tadmor:
  Non-oscillatory central schemes for one- and two-dimensional MHD equations. II: high-order semi-discrete schemes.
• 2005-045 Eitan Tadmor, Michel Rascle, and Patrizia Bagnerini:
  Compensated compactness for 2D conservation laws.
• 2005-044 Eitan Tadmor and Terence Tao:
  Velocity averaging, kinetic formulations and regularizing effects in quasilinear PDEs.
• 2005-043 Riccardo Fazio and Giovanni Russo:
  A Lagrangian central scheme for interface problems.
• 2005-042 F. Bouchut, H. Ounaissa, and B. Perthame:
  Upwinding of source term at interfaces for Euler equations with high friction.
• 2005-041 Jakov Foukzon:
  New scenario for transition to slow 3-D turbulence.
• 2005-040 Mostafa Bendahmane, Giuseppe Maria Coclite, and Kenneth H. Karlsen:
  H¹-perturbations of smooth solutions for a weakly dissipative hyperelastic-rod wave equation.
• 2005-039 W. Shen and M. Park:
  Optimal tracing of viscous shocks in solutions of viscous conservation laws.
• 2005-038 Bruno Lombard and Joel Piraux:
  Modeling 1-D elastic P-waves in a fractured rock with hyperbolic jump conditions.
• 2005-037 V.G. Danilov, D. Mitrovic, and J. Susic:
  A note on the shock wave formation process for scalar conservation laws.
• 2005-036 Youngsoo Ha and Yong-Jung Kim:
  Explicit solutions of a convection-reaction equation and defects of difference schemes.
• 2005-035 Jiequan Li, Tong Zhang, and Yuxi Zheng:
  Simple waves and a characteristic decomposition of the two dimensional compressible Euler equations.
• 2005-034 Helge Holden, Kenneth H. Karlsen, and Nils Henrik Risebro:
  Convergent difference schemes for the Hunter–Saxton equation.
• 2005-033 Xiaqi Ding:
  On a lemma Of DiPerna And Chen.
• 2005-032 Laura V. Spinolo:
  Vanishing viscosity solutions of a 2×2 triangular hyperbolic system with Dirichlet conditions on two boundaries.
• 2005-031 P. Zhang, S. C. Wong, and C.-W. Shu:
  A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway.
• 2005-030 P. Zhang, R. X. Liu, S. C. Wong, and S. Q. Dai:
  Hyperbolicity and kinematic waves of a class of multi-population partial differential equations.
• 2005-029 Wenjun Sun, Song Jiang, and Zhenhua Guo:
  Helically symmetric solutions to the 3-D Navier-Stokes equations for compressible isentropic fluids.
• 2005-028 G. M. Coclite and K. H. Karlsen:
  On the well-posedness of the Degasperis-Procesi equation.
• 2005-027 Maria Lukacova-Medvidova, Sebastian Noelle, and Marcus Kraft:
  Well-balanced finite volume evolution Galerkin methods for the shallow water equations.
• 2005-026 Francois Bouchut and Hermano Frid:
  Finite difference schemes with cross derivatives correctors for multidimensional parabolic systems.
• 2005-025 Matania Ben-Artzi, Jiequan Li, and Gerald Warnecke:
  A direct Eulerian GRP scheme for compressible fluid flows.
• 2005-024 Shi Jin and Xin Wen:
  Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with transmissions and reflections.
• 2005-023 Shi Jin and Xin Wen:
  Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds.
• 2005-022 Shi Jin and Xin Wen:
  Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials.
• 2005-021 T.R. Hagen, J. M. Hjelmervik, K-A. Lie, J.R. Natvig, and M. Ofstad Henriksen:
  Visual simulation of shallow-water waves.
• 2005-020 Sebastian Noelle, Normann Pankratz, Gabriella Puppo, and Jostein R. Natvig:
  Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows.
• 2005-019 Christian Rohde and Wen-An Yong:
  The nonrelativistic limit in radiation hydrodynamics: I. Weak entropy solutions for a model problem.
• 2005-018 Alberto Bressan and Massimo Fonte:
  An optimal transportation metric for solutions of the Camassa-Holm equation.
• 2005-017 G. M. Coclite and K. H. Karlsen:
  A singular limit problem for conservation laws related to the Camassa–Holm shallow water equation.
• 2005-016 Alberto Bressan and Adrian Constantin:
  Global conservative solutions of the Camassa–Holm equation.
• 2005-015 Jean-Francois Coulombel:
  Stability of finite difference schemes for hyperbolic systems in two space dimensions.
• 2005-014 Peter Howard and Mohammadreza Raoofi:
  Pointwise asymptotic behavior of perturbed viscous shock profiles.
• 2005-013 Bachir Ben Moussa:
  On the convergence of SPH method for scalar conservation laws with boundary conditions.
• 2005-012 E. Yu. Panov and V. M. Shelkovich:
  δⁿ-shock wave as a new type solutions of hyperbolic systems of conservation laws.
• 2005-011 Yuxi Zheng:
  Two-dimensional regular shock reflection for the pressure gradient system of conservation laws.
• 2005-010 Alberto Bressan and Yuxi Zheng:
  Conservative Solutions to a Nonlinear Variational Wave Equation.
• 2005-009 Alberto Bressan, Helge Kristian Jenssen and Paolo Baiti:
  An Instability of the Godunov Scheme.
• 2005-008 Giuseppe M. Coclite, Helge Holden and Kenneth H. Karlsen:
  Global weak solutions to a generalized hyperelastic-rod wave equation.
• 2005-007 Giuseppe M. Coclite, Helge Holden and Kenneth H. Karlsen:
  Wellposedness for a parabolic-elliptic system.
• 2005-006 Alberto Bressan and Adrian Constantin:
  Global solutions of the Hunter–Saxton equation.
• 2005-005 Marek Brandner and Stanislav Míka:
  Wave decomposition in Riemann problems for heterogeneous media.
• 2005-004 Helge Holden and Xavier Raynaud:
  A convergent numerical scheme for the Camassa–Holm equation based on multipeakons.
• 2005-003 M. V. Korobkov and E. Yu. Panov:
  On isentropic solutions of first-order quasilinear equations.
• 2005-002 E. Yu. Panov:
  On correctness classes of locally bounded generalized entropy solutions to Cauchy problem for first order quasilinear equations.
• 2005-001 E. Yu. Panov:
  Existence of strong traces for generalized solutions of multidimensional scalar conservation laws.

2004 Preprints

• 2004-074 P.G LeFloch and V. Shelukhin:
  Symmetries and global solvability of the isothermal gas dynamics equations.
• 2004-073 P.G LeFloch and M. Shearer:
  Nonclassical Riemann solvers with nucleation.
• 2004-072 N. Bedjaoui, C. Klingenberg, and P.G. LeFloch:
  On the validity of the Chapman-Enskog expansion for shock waves with small strength.
• 2004-071 J. Härterich and K. Sakamoto:
  Front motion in viscous conservation laws with stiff source terms.
• 2004-070 A. E. Tzavaras:
  Relative entropy in hyperbolic relaxation.
• 2004-069 G.-Q. Chen and M. Feldman:
  Existence and stability of multidimensional transonic flows through an infinite nozzle of arbitrary cross-sections.
• 2004-068 G. Gagneux, R. Luce, and G. Vallet:
  A non standard free-boundary problem arising from stratigraphy.
• 2004-067 M. Brandner and S. Mika:
  On the approximation of the non-autonomous nonlinear Riemann problem.
• 2004-066 M. Portilheiro and A. E. Tzavaras:
  Hydrodynamic limits for kinetic equations and the diffusive approximation of radiative transport for acoustic waves.
• 2004-065 C. Lattanzio and A. E. Tzavaras:
  Structural properties of stress relaxation and convergence from viscoelasticity to polyconvex elastodynamics.
• 2004-064 L. Pareschi, G. Puppo, and G. Russo::
  Central Runge-Kutta schemes for hyperbolic conservation laws.
• 2004-063 L. Pareschi and G. Russo:
  Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation.
• 2004-062 J.-F. Coulombel and T. Goudon:
  The strong relaxation limit of the multidimensional isothermal Euler equations.
• 2004-061 D. Serre:
  Hyperbolic-elliptic systems of conservation laws.
• 2004-060 S. Bianchini:
  Hyperbolic limit of the Jin–Xin relaxation model.
• 2004-059 V. M. Shelkovich:
  Delta-shocks, the Rankine–Hugoniot conditions, and singular superposition of distributions.
• 2004-058 R. Loubere and M. Shashkov:
  A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods.
• 2004-057 L. Ambrosio and C. De Lellis:
  A Note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations.
• 2004-056 C. De Lellis:
  Blow-up of the BV norm in the multidimensional Keyfitz and Kranzer system.
• 2004-055 L. Ambrosio, F. Bouchut,C. De Lellis:
  Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions.
• 2004-054 C. De Lellis, F. Otto, and M. Westdickenberg:
  Minimal entropy conditions for Burgers equations.
• 2004-053 C. De Lellis and T. Rivière:
  Concentration estimates for entropy measures.
• 2004-052 L. Ambrosio and C. De Lellis:
  Existence of solutions for a class of hyperbolic systems of conservations laws in several space dimensions.
• 2004-051 C. De Lellis and F. Otto:
  Structure of entropy solutions to the Eikonal equation.
• 2004-050 C. De Lellis, F. Otto, and M. Westdickenberg:
  Structure of entropy solutions for multi-dimensional conservation laws.
• 2004-049 C. De Lellis and M. Westdickenberg:
  On the optimality of velocity averaging lemmas.
• 2004-048 J. Ehrt and J. Härterich:
  Asymptotic behavior of spatially inhomogeneous balance laws.
• 2004-047 G. Barles and E. R. Jakobsen:
  Error bounds for monotone approximation schemes for Hamilton–Jacobi–Bellman equations.
• 2004-046 E. R. Jakobsen:
  On error bounds for monotone approximation schemes for multi-dimensional Isaacs equations.
• 2004-045 A.-Y. LeRoux and M.-N. LeRoux:
  Source waves.
• 2004-044 H. K. Jenssen, G. Lyng, and M. Williams:
  Equivalence of low frequency stability conditions for multidimensional detonations in three models of combustion.
• 2004-043 Y. Liu:
  Central schemes on overlapping cells.
• 2004-042 S. Ukai, T. Yang, and H. Zhao:
  Global solutions to the Boltzmann equation with external forces.
• 2004-041 P. Howard and K. Zumbrun:
  Stability of undercompressive shock profiles.
• 2004-040 C. Rohde:
  phase transitions and sharp-interface limits for the 1d-elasticity system with non-local energy.
• 2004-039 P. Baiti, A. Bressan and H. K. Jenssen:
  Instability of Travelling Wave Profiles for the Lax–Friedrichs scheme.
• 2004-038 H. Holden and X. Raynaud:
  Convergence of a finite difference scheme for the Camassa–Holm equation.
• 2004-037 K.-A. Lie and R. Juanes:
  A front-tracking method for the simulation of three-phase flow in porous media.
• 2004-036 E. R. Jakobsen and K. H. Karlsen:
  Continuous dependence estimates for viscosity solutions of integro-PDEs.
• 2004-035 H. J. Schroll and F. Svensson:
  A bi-hyperbolic finite volume method on quadrilateral meshes.
• 2004-034 Y. Brenier:
  Order preserving vibrating strings and applications to electrodynamics and magnetohydrodynamics.
• 2004-033 V. G. Danilov:
  Remarks on the formation and decay of multidimensional shock waves.
• 2004-032 D. Zeidan, E. F. Toro and A. Slaouti:
  On the Riemann Problem for a Hyperbolic Two-Phase Flow Model.
• 2004-031 M. Bendahmane and K. H. Karlsen:
  Uniqueness of entropy solutions for doubly nonlinear anisotropic degenerate parabolic equations.
• 2004-030 Corrado Mascia and Kevin Zumbrun:
  Stability of large-amplitude shock profiles of general relaxation systems.
• 2004-029 A. St-Cyr and S. J. Thomas:
  Nonlinear operator integration factor splitting for the shallow water equations.
• 2004-028 S. Baskar and P. Prasad:
  Propagation of curved shock fronts using shock ray theory and comparison with other theories.
• 2004-027 T. Yang, H. Yu, and H. Zhao:
  Cauchy problem for the Vlasov-Poisson-Boltzmann system.
• 2004-026 T. Yang and H. Zhao:
  A half-space problem for the Boltzmann equation with specular reflection boundary condition.
• 2004-025 E. Tadmor:
  Burgers' equation with vanishing hyper-viscosity.
• 2004-024 F. Bouchut, F. James, and S. Mancini:
  Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient.
• 2004-023 G-Q. Chen and M. Torres:
  Divergence-measure fields, sets of finite perimeter, and conservation laws.
• 2004-022 S. Qamar and G. Warnecke:
  A high order kinetic flux-splitting method for the relativistic magnetohydrodynamics.
• 2004-021 S. Qamar and G. Warnecke:
  A high order kinetic flux-splitting method for the special relativistic hydrodynamics.
• 2004-020 A. Bressan, P. Zhang and Y. Zheng:
  On asymptotic variational wave equations.
• 2004-019 S. Sazhenkov:
  The genuinely nonlinear non-isotropic ultra-parabolic equation.
• 2004-018 F. Colombini, T. Luo and J. Rauch:
  Nearly Lipshitzean divergence free transport does not propagate continuity and BV regularity.
• 2004-017 F. Colombini, T. Luo and J. Rauch:
  Uniqueness and nonuniquess for nonsmooth divergence free transport.
• 2004-016 F. Colombini, T. Luo and J. Rauch:
  C¹ measure respecting maps preserve bv iff they have bounded derivative.
• 2004-015 T. Luo and J. Smoller:
  Rotating fluids with self-gravitation in bounded domains.
• 2004-014 A-Y. LeRoux and M-N. LeRoux:
  A mathematical model for hurricanes.
• 2004-013 S. Jiang and G. Ni:
  A second-order γ-model BGK scheme for multimaterial compressible flows.
• 2004-012 H. K. Jenssen and R. Young:
  Gradient driven and singular flux blowup of smooth solutions to hyperbolic conservation laws.
• 2004-011 T. Luo and T. Yang:
  Global structure and asymptotic behavior of weak solutions to flood wave equations.
• 2004-010 G. Guerra:
  Well-posedness for a scalar conservation law with singular non-conservative source.
• 2004-009 J.-F. Coulombel:
  Well-posedness of hyperbolic initial boundary value problems.
• 2004-008 J. Wang, H. Wen and T. Zhou:
  On large time step Godunov scheme for hyperbolic conservation laws.
• 2004-007 M. Lewicka:
  On the well posedness for hyperbolic systems of conservation laws with large BV data.
• 2004-006 S. Sazhenkov:
  Application of the method of kinetic equation to the Darcy–Stefan problem.
• 2004-005 K. H. Karlsen and J. D. Towers:
  Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux.
• 2004-004 P. G. LeFloch and K. Trivisa:
  Continuous Glimm-type functionals and spreading of rarefaction waves.
• 2004-003 G.-Q. Chen and K. H. Karlsen:
  L^1-framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations.
• 2004-002 E. Yu. Panov:
  On isentropic solutions to first order quasilinear equations.
• 2004-001 Y. Lu:
  Some results on general system of isentropic gas dynamics.

2003 Preprints

• 2003-078 V. Danilov and D. Mitrovic:
  Weak asymptici of shock wave formation process.
• 2003-077 S. Mishra:
  Convergence of upwind finite difference algorithms for scalar conservation laws with indefinite discontinuitites in the flux function.
• 2003-076 B. Toth and B. Valko:
  Perturbation of singular equilibria of hyperbolic two-component systems: a universal hydrodynamic limit.
• 2003-075 J. Fritz and B. Toth:
  Derivation of the Leroux system as the hydrodynamic limit of a two-component lattice gas.
• 2003-074 B. Toth and B. Valko:
  Onsager relations and Eulerian hydrodynamic limit for systems with several conservation laws.
• 2003-073 S. Evje and T. Flåtten:
  A mixture flux approach for accurate and robust resolution of two-phase flows.
• 2003-072 S. Evje and T. Flåtten:
  Weakly implicit numerical schemes for the two-fluid model.
• 2003-071 S. Evje and T. Flåtten:
  CFL-free numerical schemes for the two-fluid model.
• 2003-070 S. Evje and T. Flåtten:
  Comparison of various AUSM type schemes for the two-fluid model.
• 2003-069 A. Bressan and W. Shen:
  Semi-cooperative strategies for differential games.
• 2003-068 V. G. Danilov and V. M. Shelkovich:
  dynamics of propagation and interaction of delta-shock waves in conservation law systems.
• 2003-067 H. K. Jenssen and G. Lyng:
  Low Frequency Stability of Multi-dimensional Inviscid Planar Detonation Waves.
• 2003-066 Y. Lu:
  Existence of global entropy solutions to Euler equations of compressible fluid flow.
• 2003-065 S. Schecter and P. Szmolyan:
  Composite waves in the Dafermos regularization.
• 2003-064 S Zhao and G.W. Wei:
  High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces.
• 2003-063 H. Frid and V. Shelukhin:
  Initial boundary value problems for a quasilinear parabolic system in three-phase capillary flow in porous media.
• 2003-062 J. Balbas, E. Tadmor, and C.-C. Wu:
  Non-oscillatory central schemes for one- and two-dimensional MHD equations. I.
• 2003-061 T. Kröger and S. Noelle:
  Numerical comparison of the method of transport to a standard scheme.
• 2003-060 T. Kröger, S. Noelle, and S. Zimmermann:
  On the connection between some Riemann-Solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws.
• 2003-059 V. M. Shelkovich:
  A specific hyperbolic system of conservation laws admitting delta-shock wave type solutions.
• 2003-058 C. Mascia and K. Zumbrun:
  Stability of large-amplitude shock profiles for general relazation systems.
• 2003-057 C. Mascia and K. Zumbrun:
  Stability of large-amplitude viscous shock profiles of hyperbolic-parabolic systems.
• 2003-056 G. M. Coclite:
  Control problems for systems of conservation law.
• 2003-055 F. De Vuyst and P. Jaisson:
  PDE fluid modeling of multithread systems and optimal control.
• 2003-054 D. Hoff and H. K. Jenssen:
  Symmetric nonbarotropic flows with large data and forces.
• 2003-053 H. Frid and M. Perepelitsa:
  Spatially periodic solutions in relativistic isentropic gas dynamics.
• 2003-052 V. G. Danilov and V. M. Shelkovich:
  Delta-shock wave type solution of hyperbolic systems of conservation laws.
• 2003-051 S. Schecter:
  Existence of Dafermos profiles for singular shocks.
• 2003-050 H. Guillard and A. Murrone:
  A five equation reduced model for compressible two phase flow problems.
• 2003-049 Adimurthi and G.D.Veerappa Gowda:
  Neumann boundary conditions for Hamliton Jacobi equations in a quarter plane.
• 2003-048 E.Yu.Panov:
  On the problem of symmetrizability for hyperbolic systems of first order.
• 2003-047 M. Lukacova-Medvidova, J. Saibertova, G. Warnecke, and Y. Zahaykah:
  On evolution Galerkin methods for the Maxwell and the linearized Euler equations.
• 2003-046 M. Lukacova-Medvidova, G. Warnecke, and Y. Zahaykah:
  On the boundary conditions for EG-methods applied to the two-dimensional wave equation system.
• 2003-045 M. Lukacova-Medvidova, G. Warnecke, and Y. Zahaykah:
  Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system.
• 2003-044 E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein, and B. Perthame:
  A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows.
• 2003-043 B. N. Azarenok and T. Tang:
  Second-order Godunov-type scheme for reactive flow calculations on moving meshes.
• 2003-042 A. Bressan and T. Yang:
  On the convergence rate of vanishing viscosity approximations.
• 2003-041 G. M. Coclite and H. Holden:
  Stability of solutions of quasilinear parabolic equations.
• 2003-040 E. R. Jakobsen and K. H. Karlsen:
  A "maximum principle for semicontinuous functions" applicable to integro-partial differential equations.
• 2003-039 M. Bendahmane and K. H. Karlsen:
  Renormalized entropy solutions for quasilinear anisotropic degenerate parabolic equations.
• 2003-038 H. Frid:
  Asymptotic stability of non-planar Riemann solutions for a special class of multi-d systems of conservation laws.
• 2003-037 B. Ben Moussa and A. Szepessy:
  Scalar conservation laws with boundary conditions and rough data measure solutions.
• 2003-036 H. Tang and G. Warnecke:
  A class of high resolution schemes for hyperbolic conservation laws and convection–diffusion equations with varying time and space grids.
• 2003-035 H. Tang and G. Warnecke:
  A note on (2k+1)-point conservative monotone schemes.
• 2003-034 H. Tang and G. Warnecke:
  A class of high resolution difference schemes for nonlinear Hamilton-Jacobi equations with varying time and space grids.
• 2003-033 M. Lewicka:
  Stability conditions for strong rarefaction waves
• 2003-032 M. Lewicka:
  Lyapunov functional for solutions of systems of conservation laws containing a strong rarefaction.
• 2003-031 H. Tang:
  A moving mesh method for the Euler flow calculations using a directional monitor function.
• 2003-030 A. Bressan and T. Yang:
  A sharp decay estimate for positive nonlinear waves.
• 2003-029 W. Wanzhi, S. Jiang, and Y. Shourong:
  MOCL - An algorithm for tracking interfaces in two-dimensional Eulerian codes.
• 2003-028 Y. Brenier:
  Hydrodynamic structure of the augmented Born-Infeld equations.
• 2003-027 L. Gosse and P. A. Markowich:
  Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice; I. Homogeneous problems; vanishing exterior potentials.
• 2003-026 D. Zeidan, E. Toro and A. Slaouti:
  Numerical simulation of compressible two-phase flow model based on the Riemann problem.
• 2003-025 S. Jin and S. Osher:
  A level set method for the computation of multivalued solutions to quasi-linear hyperbolic PDEs and Hamilton-Jacobi equations.
• 2003-024 F. Huang and H. Zhao:
  On the global stability of contact discontinuity for compressible Navier-Stokes equations.
• 2003-023 G. M. Coclite and N. H. Risebro:
  Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients.
• 2003-022 K. H. Karlsen, N. H. Risebro and J. D. Towers:
  L¹ stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients.
• 2003-021 A. Bressan and W. Shen:
  Small BV solutions of hyperbolic non-cooperative differential games.
• 2003-020 J.-F. Coulombel and P. Secchi:
  The stability of compressible vortex sheets in two space dimensions.
• 2003-019 N. Andrianov and G. Warnecke:
  On the solution to the Riemann problem for the compressible duct flow.
• 2003-018 F. Huang, A. Matsumura and X. Shi:
  On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary.
• 2003-017 K. H. Karlsen, N. H. Risebro, and J. D. Towers:
  Front tracking for scalar balance equations.
• 2003-016 M. Kunik, S. Qamar, and G. Warnecke:
  A reduction of the Boltzmann-Peierls equation.
• 2003-015 D. Amadori, L. Gosse, and G. Guerra:
  Godunov-type approximation for a general resonant balance law with large data.
• 2003-014 A. Bressan:
  A lemma and a conjecture on the cost of rearrangements.
• 2003-013 A. Bressan:
  An ill posed Cauchy problem for a hyperbolic system in two space dimensions.
• 2003-012 F. De Vuyst:
  Stable and accurate hybrid finite volume methods based on pure convexity arguments for hyperbolic systems of conservation law.
• 2003-011 E. R. Jakobsen:
  On the rate of convergence of approximation schemes for Bellman equations associated with optimal stopping time problems.
• 2003-010 E. R. Jakobsen:
  $W^{2,\infty}$ regularizing effect in a nonlinear, degenerate parabolic equation in one space dimension.
• 2003-009 E. R. Jakobsen:
  Error bounds for monotone approximation schemes for non-convex degenerate elliptic equations in $\mathbb{R}^1$.
• 2003-008 P. Goatin and P. LeFloch:
  The Riemann problem for a class of resonant hyperbolic systems of balance laws.
• 2003-007 Withdrawn by the author.
• 2003-006 R. Bürger, K. H. Karlsen, N. H. Risebro, and J. D. Towers:
  Well-posedness in $BV_t$ and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units.
• 2003-005 T. C. Sideris, B. Thomases, and D. Wang:
  Long time behavior of solutions to the 3D compressible Euler equations with damping.
• 2003-004 M. Kunik, S. Qamar, and G. Warnecke:
  BGK-type kinetic flux vector splitting scheme for the ultra-relativistic Euler equations.
• 2003-003 W.-A. Yong:
  An entropy condition and global existence result for hyperbolic balance laws.
• 2003-002 R. Loubere, J. Ovadia, and R. Abgrall:
  A Lagrangian discontinous Galerkin type method on unstructured meshes to solve hydrodynamics problems.
• 2003-001 G.-Q. Chen:
  Some recent methods for partial differential equations of divergence form.

2002 Preprints

• 2002-059 Y. H. Sun, Y. C. Zhou, and G. W. Wei:
  A practical spectral method for hyperbolic conservation laws.
• 2002-058 C. Mascia and K. Zumbrun:
  Pointwise Green's function bounds for shock profiles of systems with real viscosity.
• 2002-057 F. De Vuyst, J.-M- Ghidaglia, and G. Le Coq:
  On the numerical simulation of multiphase flows with changes of phase and strong gradients using the homogeneous equilibrium model.
• 2002-056 G. M. Coclite and N. H. Risebro:
  Conservation laws with time dependent discontinuous coefficients.
• 2002-055 H. Frid:
  Asymptotic stability of Riemann solutions for a class of multi-d viscous systems of conservation laws.
• 2002-054 B. Hanouzet and R. Natalini:
  Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy.
• 2002-053 M. Lukacova-Medvidova, K.W. Morton, and G.Warnecke:
  Finite volume evolution Galerkin (FVEG) methods for hyperbolic systems.
• 2002-052 G.-Q. Chen and D. Wagner:
  Global entropy solutions to exothermically reacting, compressible Euler equations.
• 2002-051 F. Bouchut:
  An antidiffusive entropy scheme for monotone scalar conservation laws.
• 2002-050 Not available
• 2002-049 E. Yu. Panov:
  On kinetic formulation of measure valued and strong measure valued solutions.
• 2002-048 N. Andrianov and G. Warnecke:
  The Riemann problem for the Baer-Nunziato model of two-phase flows.
• 2002-047 S. Schecter, B. J. Plohr, and D. Marchesin:
  Computation of Riemann solutions using the Dafermos regularization and continuation.
• 2002-046 S. Berres, R. Bürger, and K. H. Karlsen:
  Central schemes and systems of conservation laws with discontinuous coefficients modeling gravity separation of polydisperse suspensions.
• 2002-045 S. Berres, R. Bürger, and E. M. Tory:
  Mathematical model and numerical simulation of the liquid fluidization of polydisperse solid particle mixtures.
• 2002-044 Removed by request from the authors
• 2002-043 R. M. Colombo and A. Groli:
  On the optimization of a conservation law.
• 2002-042 J.-F. Coulombel:
  Weakly stable multi-d shocks.
• 2002-041 C. Lattanzio and P. Marcati:
  Global well-posedness and relaxation limits of a model for radiating gas.
• 2002-040 M. Kunik, S. Qamar, and G. Warnecke:
  Kinetic schemes for the relativistic gas dynamics.
• 2002-039 M. Kunik, S. Qamar, and G. Warnecke:
  Kinetic schemes for the ultra-relativistic Euler equations.
• 2002-038 G.-Q. Chen and M. Feldman:
  Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type.
• 2002-037 G.-Q. Chen and H. Frid:
  Extended divergence-measure fields and the Euler equations for gas dynamics.
• 2002-036 F. Huang and Z. Wang:
  Convergence of viscosity solutions for isothermal gas dynamics.
• 2002-035 F. Huang:
  Weak solution to pressureless type system.
• 2002-034 K. H. Karlsen, C. Klingenberg, and N. H. Risebro:
  A relaxation scheme for conservation laws with a discontinuous coefficient.
• 2002-033 F. Huang, A. Matsumura, and X. Shi:
  A gas-solid free boundary problem for compressible viscous gas.
• 2002-032 F. Huang, A. Matsumura, and X. Shi:
  Viscous shock wave and boundary layer solution to an inflow problem for compressible viscous gas.
• 2002-031 J.-F. Coulombel:
  Stability of multidimensional undercompressive shock waves.
• 2002-030 F. Bouchut:
  A reduced stability condition for nonlinear relaxation to conservation laws.
• 2002-029 F.R. Guarguaglini, V. Milisic, and A. Terracina:
  A discrete BGK approximation for strongly degenerate parabolic problems with boundary conditions.
• 2002-028 M. Laforest:
  A posteriori error estimate for front-tracking for nonlinear systems of conservation laws.
• 2002-027 F. Ancona and G. M. Coclite:
  On the attainable set for temple class systems with boundary controls.
• 2002-026 R. Bürger, K. H. Karlsen, N. H. Risebro, and J. D. Towers:
  On a model for continuous sedimentation in vessels with discontinuously varying cross-sectional area.
• 2002-025 S. Berres, R. Bürger, K. H. Karlsen, and E. M. Tory:
  Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression.
• 2002-024 P. Goatin:
  One sided estimates and uniqueness for hyperbolic systems of balance laws.
• 2002-023 F. Berthelin and F. Bouchut:
  Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy.
• 2002-022 M. J. Berger, C. Helzel, and R. J. LeVeque:
  H-box methods for the approximation of hyperbolic conservation laws on irregular grids.
• 2002-021 Z. Zhang and T. Tang:
  An adaptive mesh redistribution algorithm for convection-dominated problem.
• 2002-020 S. Schecter:
  Undercompressive shock waves and the Dafermos regularization.
• 2002-019 X.-B. Lin and S. Schecter:
  Stability of self-similar solutions of the Dafermos regularization of a system of conservation laws.
• 2002-018 J. Li, M. Lukacova-Medvidova, and G. Warnecke:
  Evolution galerkin schemes applied to the two-dimensional Riemann problems for the wave equation system.
• 2002-017 M. Lukacova-Medvidova, J. Saibertova, and G. Warnecke:
  Finite volume evolution Galerkin methods for nonlinear hyperbolic systems.
• 2002-016 B. N. Azarenok, S. A. Ivanenko, and T. Tang:
  Godunov's scheme and moving adaptive grids.
• 2002-015 H. Tang, T. Tang, and P. Zhang:
  An adaptive mesh redistribution method for nonlinear Hamilton-Jacobi equations in two- and three-dimensions.
• 2002-014 S. Tang and H. Zhao:
  Nonlinear stability of suliciu model for dynamic phase transitions.
• 2002-013 H. K. Jenssen and G. Lyng:
  Evaluation of the lopatinski determinant for multi-dimensional Euler equations.
• 2002-012 G. M. Coclite and B. Piccoli:
  Traffic flow on a road network.
• 2002-011 D. Aregba-Driollet and V. Milisic:
  Kinetic approximation of a boundary value problem for conservation laws.
• 2002-010 F. De Vuyst:
  Service time assessment in Computational Information Fluid Dynamics using level set methods.
• 2002-009 F. De Vuyst:
  Feasibility of fluid transport modelling for buffer and processing systems : Information Fluid Dynamics.
• 2002-008 S. Jiang and P. Zhang:
  Remarks on weak solutions to the Navier-Stokes equations for 2-D comprssible isothermal fluids with spherically symmetric initial data.
• 2002-007 G. W. Wei:
  Shock capturing by anisotropic diffusion oscillation reduction.
• 2002-006 D. S. Bale, R. J. LeVeque, S. Mitran, and J. A. Rossmanith:
  A wave propagation method for conservation laws and balance laws with spatially varying flux functions.
• 2002-005 A.-Y. Le Roux:
  Several applications of generalized solutions in some examples of wave propagation.
• 2002-004 F. Berthelin and F. Bouchut:
  Weak solutions for a hyperbolic system with unilateral constraint and mass loss.
• 2002-003 M. Seaid and M. K. Banda:
  A class of the relaxation schemes for two-dimensional Euler systems of gas dynamics.
• 2002-002 R. Burger, H. Frid, and K. H. Karlsen:
  On a free boundary problem for a strongly degenerate quasilinear parabolic equation with an application to a model of pressure filtration.
• 2002-001 G.-Q. Chen and D. Wang:
  The Cauchy problem for the Euler equations for compressible fluids.

2001 Preprints

• 2001-053 T. Grahs and T. Sonar:
  Discrete cell entropy inequalities for scalar conservation laws.
• 2001-052 Y. C. Zhou and G. W. Wei:
  High resolution conjugate filters for the simulation of flows.
• 2001-051 H. Liu and E. Tadmor:
  Spectral dynamics of the velocity gradient field in restricted flows.
• 2001-050 S. Bianchini and A. Bressan:
  Vanishing viscosity solutions of nonlinear hyperbolic systems.
• 2001-049 R. Liska and B. Wendroff:
  Comparison of several difference schemes on 1D and 2D test problems for the Euler equations.
• 2001-048 J.-F. Coulombel:
  Weak stability of non uniformly stable multidimensional shocks.
• 2001-047 E.Yu.Panov:
  On maximal and minimal generalized entropy solutions to Cauchy problem for a first-order quasilinear equation.
• 2001-046 P. Goatin and L. Gosse:
  Decay of positive waves for $n \times n$ hyperbolic systems of balance laws.
• 2001-045 L. Gosse:
  A nonconservative numerical approach for hyperbolic systems with source terms: the Well-Balanced schemes.
• 2001-044 Y. C. Zhou, Yun Gu, and G. W. Wei:
  Shock-capturing with natural high frequency oscillations.
• 2001-043 B. N. Azarenok and S. A. Ivanenko:
  Application of moving adaptive grids for numerical solution of 2-d nonstationary problems in gas dynamics.
• 2001-042 B. N. Azarenok:
  Variational barrier method of adaptive grid generation in hyperbolic problem of gas dynamics.
• 2001-041 R. Bürger, J. J. R. Damasceno, and K. H. Karlsen:
  A mathematical model for batch and continuous thickening of flocculent suspensions in vessels with varying cross section.
• 2001-040 R. Bürger, K. H. Karlsen, N. H. Risebro, and J. D. Towers:
  Numerical methods for the simulation of continuous sedimentation in ideal clarifier-thickener units.
• 2001-039 R. Li, T. Tang, and P.-W. Zhang:
  A moving mesh finite element algorithm for singular problems in two and three space dimensions.
• 2001-038 T. Tang, Z.-H. Teng, and Z.-P. Xin:
  Fractional rate of convergence for viscous approximation tononconvex conservation laws.
• 2001-037 M. Banda and M. Seaid:
  Higher-order relaxation schemes for hyperbolic systems of conservation laws.
• 2001-036 R. J. LeVeque:
  Some traffic flow models illustrating interesting hyperbolic behavior.
• 2001-035 R. J. LeVeque:
  Finite volume methods for nonlinear elasticity in heterogeneous media.
• 2001-034 Guy Barles and Espen R. Jakobsen:
  On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations.
• 2001-033 A. Bressan and G. M. Coclite:
  On the boundary control of systems of conservation laws.
• 2001-032 K.-A. Lie and S. Noelle:
  On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws.
• 2001-031 K.-A. Lie and S. Noelle:
  An improved quadrature rule for the flux-computation in staggered central difference schemes in multidimensions.
• 2001-030 N. Andrianov, R. Saurel, and G. Warnecke:
  A simple method for compressible multiphase mixtures and interfaces.
• 2001-029 E. R. Jakobsen and K. Hvistendahl Karlsen:
  Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations.
• 2001-028 J. Pan and G. Warnecke:
  Asymptotic stability of traveling waves for viscous conservation laws with dissipation.
• 2001-027 C. Mascia and K. Zumbrun:
  Pointwise Green's function bounds and stability of relaxation shocks.
• 2001-026 F. Huang and Z. Wang:
  Well posedness for pressureless flow.
• 2001-025 J. Li and G. Warnecke:
  Generalized characteristics and the uniqueness of entropy solutions to zero-pressure gas dynamics.
• 2001-024 J. Huang, J. Wang, and G. Warnecke:
  Error bounds for the large time step Glimm scheme applied to scalar conservation laws.
• 2001-023 J. Wang and G. Warnecke:
  Existence and uniqueness of solutions for a non-uniformly parabolic equation.
• 2001-022 K. H. Karlsen, N. H. Risebro, and J. D. Towers:
  Convergence of an upwind difference scheme for degenerate parabolic convection-diffusion equations with a discontinuous coefficient.
• 2001-021 R. Bürger, K. H. Karlsen, C. Klingenberg, and N. H. Risebro:
  A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units.
• 2001-020 Y. G. Rykov:
  On the nonhamilton character of shocks in 2-D pressureless gas.
• 2001-019 R. Bürger, K. H. Karlsen, E. M. Tory, and W. L. Wendland:
  Model equations and instability regions for the sedimentation of polydisperse suspensions of spheres.
• 2001-018 K. Xu:
  A well-balanced gas-kinetic scheme for the shallow water equations with source terms.
• 2001-017 L. Gosse:
  Localization effects and measure source terms in numerical schemes for balance laws.
• 2001-016 Y.-X. Kan, T. Tang, and Z.-H. Teng:
  On the piecewisely smooth solutions to non-homogeneous scalar conservation laws.
• 2001-015 H. Fan and S. Jin:
  Front motion in muti-dimensional conservation laws with stiff source terms driven by mean curvature and variation of front thickness.
• 2001-014 H.-Z. Tang and T. Tang:
  Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws.
• 2001-013 K. H. Karlsen, N. H. Risebro, and J. D. Towers:
  On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient.
• 2001-012 M. Radyna:
  Functionals with values in the non-Archimedean field of Laurent series and method for numerical calculations of shocks and soliton like solutions of some conservation laws.
• 2001-011 Kun Xu:
  A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method.
• 2001-010 G. Puppo:
  Numerical entropy production for central schemes.
• 2001-009 M. Küther:
  A priori and a posteriori error estimates for the staggered Lax-Friedrichs scheme in multi-dimensions for scalar nonlinear conservation laws.
• 2001-008 S. Evje and K. H. Karlsen:
  An error estimate for viscous approximate solutions of degenerate parabolic equations.
• 2001-007 V. Milisic:
  Stability and convergence of discrete kinetic approximations to an initial-boundary value problem for conservation laws.
• 2001-006 P. Baiti and H. K. Jenssen:
  Blowup in $L^{\infty}$ for a class of genuinely nonlinear hyperbolic systems of conservation laws.
• 2001-005 S. Jiang and P. Zhang:
  Axisymmetric solutions of the 3-D Navier-Stokes equations for compressible isentropic fluids.
• 2001-004 E. R. Jakobsen and K. Hvistendahl Karlsen:
  Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations.
• 2001-003 K. Hvistendahl Karlsen and M. Ohlberger:
  A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations.
• 2001-002 R. J. LeVeque and M. Pelanti:
  A class of approximate Riemann solvers and their relation to relaxation schemes.
• 2001-001 J.D. Towers:
  TVD schemes for two-dimensional scalar conservation laws.

2000 Preprints

• 2000-050 D. Amadori, L. Gosse, and G. Guerra:
  Global BV entropy solutions and uniqueness for hyperbolic systems of balance laws.
• 2000-049 K.-A. Lie and S. Noelle:
  High resolution nonoscillatory central difference schemes for the 2D Euler equations via artificial compression.
• 2000-048 F. Ancona and P. Goatin:
  Uniqueness and stability of $l^\infty$ solutions for Temple class systems with boundary and properties of the attainable sets.
• 2000-047 C. Mascia, A. Porretta, and A. Terracina:
  Nonhomogeneous Dirichlet problems for degenerate parabolic-hyperbolic equations.
• 2000-046 D. Aregba-Driollet, R. Natalini, and S.Q. Tang:
  Diffusive kinetic explicit schemes for nonlinear degenerate parabolic systems.
• 2000-045 D. Donatelli and P. Marcati:
  Convergence of singular limits for multi-d semilinear hyperbolic systems to parabolic systems.
• 2000-044 F. Guarguaglini and A. Terracina:
  A BGK approximation to nonlinear parabolic initial-boundary value problems.
• 2000-043 F. Huang:
  Global existence of weak solution for a nonstrictly hyperbolic system of conservation laws.
• 2000-042 F. Bouchut:
  Entropy satisfying flux vector splittings and kinetic BGK models.
• 2000-041 R. Bürger, F. Concha, and K. H. Karlsen:
  Phenomenological model of filtration processes: 1. Cake formation and expression.
• 2000-040 J. Qian and W. W. Symes:
  Finite-difference quasi-P traveltimes for anisotropic media.
• 2000-039 J. Qian and W. W. Symes:
  An adaptive finite-difference method for traveltimes and amplitudes.
• 2000-038 S. Bianchini and A. Bressan:
  A case study in vanishing viscosity.
• 2000-037 A. Kurganov and E. Tadmor:
  Solution of two-dimensional Riemann problems for gas dynamics.
• 2000-036 S. Bianchini and R. M. Colombo:
  On the stability of the standard Riemann semigroup.
• 2000-035 K. H. Karlsen and N. H. Risebro:
  Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients.
• 2000-034 L. Gosse and F. James:
  Convergence results for an inhomogeneous system arising in various high frequency approximations.
• 2000-033 F. Ancona and A. Marson:
  A wave front tracking algorithm for NxN non genuinely nonlinear conservation laws.
• 2000-032 C. Lattanzio and R. Natalini:
  Convergence of diffusive BGK approximations for nonlinear strongly parabolic systems.
• 2000-031 M. S. Espedal and K. Hvistendahl Karlsen:
  Numerical solution of reservoir flow models based on large time step operator splitting algorithms.
• 2000-030 John D. Towers:
  A difference scheme for conservation laws with a discontinuous flux - the nonconvex case.
• 2000-029 G. Godinaud, A.-Y. Le Roux, and M.-N. Le Roux:
  Generation of new solvers involving the source term for a class of non homogeneous hyperbolic systems.
• 2000-028 E. R. Jakobsen, K. H. Karlsen, and N. H. Risebro:
  On the convergence rate of operator splitting for weakly coupled systems of Hamilton-Jacobi equations.
• 2000-027 T. Tang:
  Error estimates for approximate solutions for nonlinear scalar conservation laws.
• 2000-026 F. Berthelin and F. Bouchut:
  Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics.
• 2000-025 F. Berthelin and F. Bouchut:
  Solution with finite energy to a BGK system relaxing to isentropic gas dynamics.
• 2000-024 H. K. Jenssen and C. Sinestrari:
  On the spreading of characteristics for nonconvex conservation laws.
• 2000-023 R. Bürger and K. Hvistendahl Karlsen:
  A strongly degenerate convection-diffusion problem modeling centrifugation of flocculated suspensions.
• 2000-022 S. Evje, K. Hvistendahl Karlsen, and N. H. Risebro:
  A continuous dependence result for nonlinear degenerate parabolic equations with spatially dependent flux function.
• 2000-021 K.-A. Lie and S. Noelle:
  Remarks on high-resolution non-oscillatory central schemes for multi-dimensional systems of conservation laws. Part I: An improved quadrature rule for the flux-computation.
• 2000-020 S. Jiang and P. Zhang:
  On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations.
• 2000-019 H. Li, P. Markowich, and M. Mei:
  Asymptotic behavior of solutions of the hydrodynamic model of semiconductors.
• 2000-018 P. Marcati, M. Mei, and B. Rubino:
  Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping.
• 2000-017 K. Hvistendahl Karlsen and N.H. Risebro:
  Unconditionally stable methods for Hamilton-Jacobi equations.
• 2000-016 John D. Towers:
  A difference scheme for conservation laws with a discontinuous flux - the nonconvex case.
• 2000-015 K. Hvistendahl Karlsen and N.H. Risebro:
  On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients.
• 2000-014 H. Hanche-Olsen, H. Holden, and N.H. Risebro:
  The Riemann problem for an elastic string with a linear Hooke's law.
• 2000-013 G. Chiavassa and R. Donat:
  Numerical experiments with point value multiresolution for 2D compressible flows.
• 2000-012 De-xing Kong:
  Life-span of classical solutions to quasilinear hyperbolic systems with slow decay initial data.
• 2000-011 K. Xu and H.-Z. Tang:
  An explanation for the sonic point glitch.
• 2000-010 R. Bürger and K. Hvistendahl Karlsen:
  On some upwind difference schemes for the phenomenological sedimentation-consolidation model.
• 2000-009 A. Bressan and H. K. Jenssen:
  On the convergence of Godunov scheme for nonlinear hyperbolic systems.
• 2000-008 R. Bürger, K.-K. Fjelde, K. Höfler, and K. Hvistendahl Karlsen:
  Central difference solutions of the kinematic model of settling of polydisperse suspensions and three-dimensional particle-scale simulations.
• 2000-007 E. R. Jakobsen, K. H. Karlsen, and N. H. Risebro:
  On the convergence rate of operator splitting for Hamilton-Jacobi equations with source terms.
• 2000-006 B. Wendroff:
  Approximate Riemann solvers, Godunov schemes, and contact discontinuities.
• 2000-005 F. Bouchut, F.R. Guarguaglini, and R. Natalini:
  Diffusive BGK approximations for nonlinear multidimensional parabolic equations.
• 2000-004 R. Natalini and S. Tang:
  Discrete kinetic models for dynamical phase transitions.
• 2000-003 H. Liu and R. Natalini:
  Long-time diffusive behavior of solutions to a hyperbolic relaxation system.
• 2000-002 R. Natalini and A. Terracina:
  Convergence of a relaxation approximation to a boundary value problem for conservation laws.
• 2000-001 K. H. Karlsen, K.-A. Lie, J. R. Natvig, H. F. Nordhaug, and H. K. Dahle:
  Operator splitting methods for systems of convection-diffusion equations: nonlinear error mechanisms and correction strategies.

1999 Preprints

• 1999-045 K. H. Karlsen and N. H. Risebro:
  A note on front tracking and the equivalence between viscosity solutions of Hamilton-Jacobi equations and entropy solutions of scalar conservation laws.
• 1999-044 S. Takeno:
  Time-periodic solutions for a scalar conservation law.
• 1999-043 W. Bao and S. Jin:
  The random projection method for stiff detonation waves.
• 1999-042 W. Bao and S. Jin:
  Error estimates on the random projection methods for hyperbolic systems with stiff reaction terms.
• 1999-041 W. Bao and S. Jin:
  The random projection method for hyperbolic systems with stiff reaction terms.
• 1999-040 S. Jin and M. Katsoulakis:
  Hyperbolic systems with supercharacteristic relaxations and roll waves.
• 1999-039 H. Holden, K. H. Karlsen, and K.-A. Lie:
  Operator splitting methods for degenerate convection-diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation.
• 1999-038 J. Härterich:
  Viscous profiles for traveling waves of scalar balance laws: The canard case.
• 1999-037 S. Bianchini:
  On a Glimm type functional for a special Jin-Xin relaxation model.
• 1999-036 T. Tang and Z.-H. Teng:
  On the regularity of approximate solutions to conservation laws with piecewise smooth solutions.
• 1999-035 E. Tadmor and T. Tang:
  Pointwise error estimates for relaxation approximations to conservation laws.
• 1999-034 A. Bressan and W. Shen:
  BV estimates for multicomponent chromatography with relaxation.
• 1999-033 S. Jiang and P. Zhang:
  Global weak solutions to the Navier-Stokes equations for a 1D viscous polytropic ideal gas.
• 1999-032 H. Holden, K. H. Karlsen, and K.-A. Lie:
  Operator splitting methods for degenerate convection-diffusion equations I: convergence and entropy estimates.
• 1999-031 K. Xu and Z. Li:
  Gas evolution dynamics and numerical dissipation in shock capturing schemes.
• 1999-030 S. Bianchini and A. Bressan:
  On a Lyapunov functional relating shortening curves and viscous conservation laws.
• 1999-029 C. Mascia:
  First order singular perturbations of quasilinear nonconvex type.
• 1999-028 S. Noelle:
  The MoT-ICE: a new high-resolution wave-propagation algorithm for multi-dimensional systems of conservation laws based on Fey's Method of Transport.
• 1999-027 C. Mascia and A. Terracina:
  Large time behavior for conservation laws with source in a bounded domain.
• 1999-026 G. Chen and M. Rascle:
  Initial layers and uniqueness of weak entropy conservation laws.
• 1999-025 P. Hoch and M. Rascle:
  Hamilton-Jacobi equation on a manifold, and applications to mesh generation or refinement.
• 1999-024 J. Towers:
  Convergence of a difference scheme for conservation laws with a discontinuous flux.
• 1999-023 K.-K. Fjelde and K. Hvistendahl Karlsen:
  High-resolution hybrid primitive-conservative upwind schemes for the drift flux model.
• 1999-022 R. Bürger, S. Evje, and K. Hvistendahl Karlsen:
  On strongly degenerate convection-diffusion problems modeling sedimentation-consolidation processes.
• 1999-021 A. N. Chinnayya and A.-Y. Le Roux:
  A New general Riemann solver for the shallow water equations, with friction and topography.
• 1999-020 A. Rezgui:
  An analysis of accuracy and convergence of finite volume methods.
• 1999-019 R. Balean:
  Granular avalanche flow down a smoothly varying slope: the existence of entropy solutions.
• 1999-018 H.L. Liu and G. Warnecke:
  Convergence rates for relaxation schemes approximating conservation laws.
• 1999-017 V. Haugse, K. H. Karlsen, K.-A. Lie, and J. R. Natvig:
  Numerical solution of the polymer system by front tracking.
• 1999-016 Withdrawn by the author.
• 1999-015 K. Hvistendahl Karlsen, K.-A. Lie, and N. H. Risebro:
  A fast level set method for reservoir simulation.
• 1999-014 H. Frid:
  Periodic solutions of conservation laws constructed through Glimm scheme.
• 1999-013 F. Ancona and A. Marson:
  A note on the Riemann problem for general nxn conservation laws.
• 1999-012 F. Ancona and A. Marson:
  Well-posedness for general 2x2 systems of conservation laws.
• 1999-011 A. Kurganov and E. Tadmor:
  New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• 1999-010 S. Junca and M. Rascle:
  Relaxation of the isothermal Euler-Poisson system to the drift-diffusion equations
• 1999-009 Ph. Hoch and M. Rascle:
  A numerical study of a pathological example of p-system.
• 1999-008 A. Aw and M. Rascle:
  Resurrection of "second order" models of car traffic ?
• 1999-007 C. Klingenberg and N. H. Risebro::
  Stability of a resonant system of conservation laws modeling polymer flow with gravitation
• 1999-006 R. Bürger, S. Evje, K. Hvistendahl Karlsen, and K.-A. Lie:
  Numerical methods for the simulation of the settling of flocculated suspensions
• 1999-005 R. Bürger, F. Concha, K. K. Fjelde, and K. Hvistendahl Karlsen:
  Numerical simulation of the settling of polydisperse suspensions of spheres
• 1999-004 S. Bianchini and A. Bressan:
  Vanishing viscosity solutions of hyperbolic systems on manifolds
• 1999-003 H. Holden, K. Hvistendahl Karlsen, and N. H. Risebro:
  Operator splitting methods for generalized Korteweg-de Vries equations
• 1999-002 S. H. Lui and K. Xu:
  Entropy analysis of kinetic flux vector splitting schemes for the compressible Euler equations.
• 1999-001 M. S. Espedal and K. Hvistendahl Karlsen:
  Numerical solution of reservoir flow models based on large time step operator splitting algorithms.

1998 Preprints

• 1998-042 S. Jiang:
  Large-time behavior of solutions to the equations of a one-dimensional viscous polytropic ideal gas in unbounded domains.
• 1998-041 B. Wendroff:
  A two-dimensional HLLE Riemann solver and associated Godunov-type difference scheme for gas dynamics.
• 1998-040 R. Balean:
  Granular avalanche flow down a smoothly varying slope: the existence of entropy solutions.
• 1998-039 A. Bressan and P. Goatin:
  Stability of L$^\infty$ solutions of Temple class systems.
• 1998-038 S. Jin, L. Pareschi, and G. Toscani:
  Uniformly accurate diffusive relaxation schemes for multiscale transport equations.
• 1998-037 H. Fan, S. Jin, and Z.-H. Teng:
  Zero reaction limit for hyperbolic conservation laws with source terms.
• 1998-036 D. Amadori and G. Guerra:
  Global BV solutions and relaxation limit for a system of conservation laws.
• 1998-035 R. Liska and B. Wendroff:
  Composite centered schemes for multidimensional conservation laws.
• 1998-034 F. Bouchut:
  Construction of BGK models with a family of kinetic entropies for a given system of conservation laws.
• 1998-033 A. Bressan and M. Lewicka:
  A uniqueness condition for hyperbolic systems of conservation laws.
• 1998-032 A. Bressan:
  On the Cauchy problem for nonlinear hyperbolic systems.
• 1998-031 A. Bressan:
  Hyperbolic systems of conservation laws.
• 1998-030 A. Bressan, T.-P. Liu, and T. Yang:
  L^1 stability estimates for n x n conservation laws.
• 1998-029 A. Bressan and P. G. LeFloch:
  Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws.
• 1998-028 C. Fries:
  Stability of viscous shock waves associated with non-convex modes.
• 1998-027 S. Jin and H. Liu:
  Diffusion limit of a hyperbolic system with relaxation.
• 1998-026 S. Jin, M. Katsoulakis, Z. Xin:
  Relaxation schemes for curvature-dependent front propagation.
• 1998-025 Kun Xu:
  Gas evolution dynamics in Godunov-type schemes.
• 1998-024 M. H. Zhou, M. Mascagni, and A. Y. Qiao:
  Explicit finite difference schemes for the advection equation.
• 1998-023 H. K. Jenssen:
  A note on the spreading of characteristics for nonconvex conservation laws.
• 1998-022 E. Tadmor:
  Approximate solutions of nonlinear conservation laws and related equations.
• 1998-021 C. Lattanzio and P. Marcati:
  The zero relaxation limit for $2\times 2$ hyperbolic systems.
• 1998-020 R. Fazio and R. J. LeVeque::
  Moving-mesh methods for one-dimensional hyperbolic problems using CLAWPACK.
• 1998-019 R. Holdahl, H. Holden, and K.-A. Lie:
  Unconditionally stable splitting methods for the shallow water equations.
• 1998-018 H. Holden, K.-A. Lie, and N. H. Risebro:
  An unconditionally stable method for the Euler equations.
• 1998-017 S. Evje and K. Hvistendahl Karlsen:
  Discrete approximations of BV solutions to doubly nonlinear degenerate parabolic equations.
• 1998-016 E. Tadmor and T. Tassa:
  On the homogenization of oscillatory solutions to nonlinear convection-diffusion equations
• 1998-015 C.-T. Lin and E. Tadmor:
  $L^1$-stability and error estimates for approximate Hamilton-Jacobi solutions
• 1998-014 S. Evje and K. Hvistendahl Karlsen:
  Degenerate convection-diffusion equations and implicit monotone difference schemes.
• 1998-013 K. Hvistendahl Karlsen, K.-A. Lie, and N. H. Risebro:
  A front tracking method for conservation laws with boundary conditions.
• 1998-012 W. Shen, A. Tveito, and R. Winther:
  Rate of convergence for the zero relaxation limit.
• 1998-011 S. Evje and K. Hvistendahl Karlsen:
  Monotone difference approximations of BV solutions to degenerate convection-diffusion equations.
• 1998-010 J. Härterich:
  Heteroclinic orbits between rotating waves in hyperbolic balance laws.
• 1998-009 L. Pareschi and G. Naldi:
  Numerical schemes for kinetic equations in diffusive regimes.
• 1998-008 H. K. Jenssen:
  Blowup for systems of conservation laws.
• 1998-007 E. Tadmor and T. Tang:
  Pointwise error estimates for scalar conservation laws with piecewise smooth solutions.
• 1998-006 H. K. Jenssen and C. Sinestrari:
  Blowup asymptotics for scalar conservation laws with a source.
• 1998-005 T. Fogarty and R. J. LeVeque:
  High-resolution finite volume methods for acoustics in a rapidly-varying heterogeneous medium.
• 1998-004 R. J. LeVeque:
  Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propogation algorithm.
• 1998-003 K. Brusdal, H. K. Dahle, K. Hvistendahl Karlsen, and T. Mannseth:
  A study of the modelling error in two operator splitting algorithms for porous media flow.
• 1998-002 K. Hvistendahl Karlsen, K. Brusdal, H. K. Dahle, S. Evje, and K.-A. Lie:
  The corrected operator splitting approach applied to an advection-diffusion problem.
• 1998-001 W.-A. Yong:
  Singular perturbations of first-order hyperbolic systems with stiff source terms

1997 Preprints

• 1997-037 R. A. Klausen and N. H. Risebro:
  Stability of conservation laws with discontinuous coefficients
• 1997-036 R. M. Colombo and N. H. Risebro:
  Continuous dependence in the large for some equations of gas dynamics
• 1997-035 A. Bressan and P. Goatin:
  Oleinik type estimates and uniqueness for n x n conservation laws
• 1997-034 R. Liska and B. Wendroff:
  2D shallow water equations by composite schemes
• 1997-033 M. J. Berger and R. J. LeVeque:
  Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems
• 1997-032 J. Lorenz and H. J. Schroll:
  Stiff well-posedness and asymptotic expansions for hyperbolic systems with relaxation
• 1997-031 K.-A. Lie:
  A dimensional splitting method for nonlinear equations with variable coefficients
• 1997-030 K.-A. Lie:
  Front tracking for one-dimensional nonlinear advection equations with variable coefficients
• 1997-029 S. Evje, K. Hvistendahl Karlsen, K.-A. Lie, and N. H. Risebro:
  Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations
• 1997-028 S. Evje and K. Hvistendahl Karlsen:
  Viscous splitting approximation of mixed hyperbolic-parabolic convection-diffusion equations
• 1997-027 D. Amadori, B. Baiti, P. G. LeFloch, and B. Piccoli:
  Nonclassical shocks and the Cauchy problem for nonconvex conservation laws
• 1997-026 S. Jin and Z. Xin:
  Numerical passage from systems of conservation laws to Hamilton-Jacobi equations, and a relaxation scheme
• 1997-025 F. Ancona and A. Marson:
  Scalar non-linear conservation laws with integrable boundary data
• 1997-024 F. Ancona and A. Marson:
  On the attainable set for scalar non-linear conservation laws with boundary control
• 1997-023 W.-C. Lien:
  Hyperbolic conservation laws with a moving source
• 1997-022 W.-A. Yong:
  A simple approach to Glimm's interaction estimates
• 1997-021 S. Jin, L. Pareschi, and G. Toscani:
  Diffusive relaxation schemes for discrete-velocity kinetic equations
• 1997-020 S. Jin and M. Katsoulakis:
  Relaxation approximations to front propagation
• 1997-019 L. F. Henderson and R. Menikoff:
  Triple shock entropy theorem and its consequences
• 1997-018 R. Liska and B. Wendroff:
  Composite schemes for conservation laws
• 1997-017 J. P. Vila and P. Villedieu:
  Convergence of explicit finite volume schemes for Friedrichs Systems
• 1997-016 K. Hvistendahl Karlsen and K.-A. Lie:
  An unconditionally stable splitting scheme for a class nonlinear parabolic equations
• 1997-015 S. Evje and K. Hvistendahl Karlsen:
  A note on viscous splitting of degenerate convection-diffusion equations
• 1997-014 P. Marcati and B. Rubino:
  Hyperbolic to parabolic relaxation theory for quasilinear first order systems
• 1997-013 G.-S. Jiang and E. Tadmor:
  Non-oscillatory central schemes for multidimensional hyperbolic conservation laws
• 1997-012 X.-D. Liu and E. Tadmor:
  Third order nonoscillatory central scheme for hyperbolic conservation laws
• 1997-011 K. Hvistendahl Karlsen, K.-A. Lie, N.H. Risebro, and J. Frøyen:
  A front tracking approach to a two-phase fluid flow model with capillary forces
• 1997-010 K. Hvistendahl Karlsen and N.H. Risebro:
  Corrected operator splitting for nonlinear parabolic equations
• 1997-009 H.J. Schroll and A. Tveito:
  Local existence and stability for a hyperbolic–elliptic system modeling two–phase reservoir flow
• 1997-008 W.-A. Yong:
  A difference scheme for a stiff system of conservation laws
• 1997-007 W. Shen, A. Tveito, and R. Winther:
  On the zero relaxation limit for a system modeling the motions of a viscoelastic solid
• 1997-006 A. Bressan and W. Shen:
  Uniqueness for discontinuous O.D.E. and conservation laws
• 1997-005 C. Mascia:
  Qualitative behavior of conservation laws with reaction term and nonconvex flux
• 1997-004 C. Lattanzio and P. Marcati:
  The zero relaxation limit for the hydrodynamic Whitham traffic flow model
• 1997-003 J.O. Langseth and R.J. LeVeque:
  A wave propagation method for three-dimensional hyperbolic conservation laws
• 1997-002 A. Bressan, G. Crasta, and B. Piccoli:
  Well-posedness of the Cauchy problem for nxn systems of conservation laws
• 1997-001 K. Xu and J. Hu:
  Projection dynamics in Godunov-type schemes i: to the physical understanding of post-shock oscillations

1996 Preprints

• 1996-044 P. Baiti and H.K. Jenssen:
  Well-posedness for a class of $2\times 2$ conservation laws with $L^\infty$ data
• 1996-043 Alberto Bressan and Rinaldo M. Colombo:
  Decay of positive waves in nonlinear systems of conservation laws
  

• 1996-042 Alberto Bressan:
  The semigroup approach to systems of conservation laws
• 1996-041 C. Mascia and C. Sinestrari:
  The perturbed riemann problem for a balance law
• 1996-040 P. Baiti and A. Bressan:
  Lower semicontinuity of weighted path length in BV
• 1996-039 T. Luo, R. Natalini, and Z. Xin:
  Large time behavior of the solutions to a hydrodynamic model for semiconductors
• 1996-038 V. Haugse:
  Identification of mobilities for the Buckley-Leverett equation by front tracking
• 1996-037 P. Baiti and H.K. Jenssen:
  On the front tracking algorithm
• 1996-036 T. Tang:
  Convergence analysis for operator splitting methods to conservation laws with stiff source terms
• 1996-035 K. Xu:
  Unsplitting BGK-type schemes for the shallow water equations
• 1996-034 I. Gasser and R. Natalini:
  The energy transport and the drift diffusion equations as relaxation limits of the hydrodynamic model for semiconductors
• 1996-033 H. Holden and N. H. Risebro:
  Riemann problems with a kink
• 1996-032 A. Bressan and A. Marson:
  Error bounds for a deterministic version of the Glimm scheme
• 1996-031 P. Baiti and A. Bressan:
  The semigroup generated by a Temple class system with large data
• 1996-030 R. Bodenmann and H. J. Schroll:
  Higher order discretisation of initial-boundary value problems for mixed systems
• 1996-029 J. Lorenz and H. J. Schroll:
  Stiff well-posedness for hyperbolic systems with large relaxation terms
• 1996-028 R. Bodenmann and H. J. Schroll:
  Compact difference methods applied to initial-boundary value problems for mixed systems
• 1996-027 H. J. Schroll and R. Winther:
  Finite difference schemes for scalar conservation laws with source terms
• 1996-026 H. J. Schroll:
  Convergence of implicit finite difference methods applied to nonlinear mixed systems
• 1996-025 T. Tang and Z.-H. Teng:
  Viscosity methods for piecewise smooth solutions to scalar conservation laws
• 1996-024 D. Hoff:
  Discontinuous solutions of the Navier-Stokes equations for multidimensional heat-conducting flow
• 1996-023 X. Cai, H. P. Langtangen, B. F. Nielsen, and A. Tveito:
  A finite element method for fully nonlinear water waves
• 1996-022 H. J. Schroll, A. Tveito, and R. Winther:
  A system of conservation laws with a relaxation term
• 1996-021 H. J. Schroll, A. Tveito, and R. Winther:
  An error bound for a finite difference scheme applied to a stiff system of conservation laws
• 1996-020 A. Tveito and R. Winther:
  On the rate of convergence to equilibrium for a system of conservation laws including a relaxation term
• 1996-019 W. Shen, A. Tveito, and R. Winther:
  A system of conservation laws including a stiff relaxation term; the 2D case
• 1996-018 W. Shen:
  Error bounds of finite difference schemes for two-dimensional scalar conservation laws with source term
• 1996-017 A. Bressan and G. Guerra:
  Shift-differentiability of the flow generated by a conservation law
• 1996-016 C. Mascia:
  Travelling wave solutions for a balance law
• 1996-015 B. Gottschlich-Müller and S. Müller:
  Multiscale concept for conservation laws
• 1996-014 A. Bressan and P. LeFloch:
  Uniqueness of weak solutions to systems of conservation laws
• 1996-013 B. Hanouzet and R. Natalini:
  Weakly coupled systems of quasilinear hyperbolic equations
• 1996-012 R. Natalini:
  A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws
• 1996-011 C. Mascia and R. Natalini:
  L^1 nonlinear stability of travelling waves for a hyperbolic system with relaxation
• 1996-010 B. H. Gilding, R. Natalini, and A. Tesei:
  How parabolic free boundaries approximate hyperbolic fronts
• 1996-009 B. Hanouzet, R. Natalini, and A. Tesei:
  On the Chapman-Jouguet Limit for a combustion model
• 1996-008 R. Natalini and B. Rubino:
  A discrete approximation for hyperbolic systems with quadratic interaction term
• 1996-007 D. Aregba-Driollet and R. Natalini:
  Convergence of relaxation schemes for conservation laws
• 1996-006 R. Natalini:
  Convergence to equilibrium for the relaxation approximations of conservation laws
• 1996-005 P. Le Floch and R. Natalini:
  Conservation laws with vanishing nonlinear diffusion and dispersion
• 1996-004 P. Marcati and R. Natalini:
  Global weak entropy solutions to quasilinear wave equations of Klein–Gordon and Sine–Gordon Type
• 1996-003 H. Holden and N. H. Risebro:
  Conservation laws with a random source
• 1996-002 K. Hvistendahl Karlsen and N. H. Risebro:
  An operator splitting method for convection-diffusion equations
• 1996-001 K.-A. Lie, V. Haugse, and K. Hvistendahl Karlsen:
  Dimensional splitting with front tracking and adaptive local grid refinement.