## 2014 Preprints

- 2014-013

On the Cauchy problem for scalar conservation laws on the Bohr compactification of**R**^{n}. - 2014-012

On the Braess paradox with nonlinear dynamics and control theory. - 2014-011

Representation of dissipative solutions to a nonlinear variational wave equation. - 2014-010

On the Cauchy problem for scalar conservation laws in the class of Besicovitch almost periodic functions. - 2014-009

Conservation law models for traffic flow on a network of roads. - 2014-008

Continuous Riemann solvers for traffic flow at a junction. - 2014-007

Rigorous derivation of the Lighthill–Whitham–Richards model from the follow the-leader model as many particle limit. - 2014-006

Spherically symmetric solutions of multi-dimensional zero-pressure gas dynamics system. - 2014-005

Error estimates for well-balanced and time-split schemes on a damped semilinear wave equation. - 2014-004

Global existence of weak solutions for the Burgers–Hilbert equation. - 2014-003

A semigroup approach to an integro-differential equation modeling slow erosion. - 2014-002

Flows on networks: recent results and perspectives. - 2014-001

Uniqueness of conservative solutions to the Camassa–Holm equation via characteristics

## 2013 Preprints

- 2013-013

Nonexistence and nonuniqueness for multidimensional sticky particle systems. - 2013-012

Quadratic interaction functional for systems of conservation laws: a case study. - 2013-011

On a quadratic functional for scalar conservation laws. - 2013-010

Lack of BV bounds for approximate solutions to the p-system with large data. - 2013-009

On an inverse problem for scalar conservation laws. - 2013-008

On decay of periodic renormalized solutions to scalar conservation laws. - 2013-007

Coupling constants and the generalized Riemann problem for isothermal junction flow. - 2013-006

A new Runge–Kutta discontinuous Galerkin method with conservation constraint to improve CFL condition for solving conservation laws. - 2013-005

A limiting strategy for the back and forth error compensation and correction method for solving advection equations. - 2013-004

Existence and stability of traveling waves for an integro-differential equation for slow erosion. - 2013-003

A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows. - 2013-002

A two-fluid four-equation model with instantaneous thermodynamical equilibrium. - 2013-001

Transient L¹ error estimates for well-balanced schemes on non-resonant scalar balance laws.

## 2012 Preprints

- 2012-024

From polynomial integrals of Hamiltonian flows to a model of non-linear elasticity. - 2012-023

Singular solutions for a 2×2 system in nonconservative form with incomplete set of eigenvectors. - 2012-022

Error estimate for Godunov approximation of locally constrained conservation laws. - 2012-021

Initial-boundary value problems to the one-dimensional compressible Navier–Stokes equations with degenerate transport coefficients. - 2012-020

Convexity-preserving flux identification for scalar conservation laws modelling sedimentation. - 2012-019

On periodic entropy sub- and super-solutions to a degenerate elliptic-hyperbolic equation. - 2012-018

Large time step and asymptotic preserving numerical schemes for the gas dynamics equations with source terms. - 2012-017

Existence of optima and equilibria for traffic flow on networks. - 2012-016

Global solutions to the one-dimensional compressible Navier–Stokes–Poisson equations with large data. - 2012-015

Global solutions to one-dimensional shallow water magnetohydrodynamic equations. - 2012-014

Existence of global entropy solutions to the isentropic Euler equations with geometric effects. - 2012-013

Existence of global bounded weak entropy solutions to extended Keyfitz–Kranzer system modelling polymer flooding. - 2012-012

The exact Riemann solutions to shallow water equations. - 2012-011

A note on the carbuncle in shallow water simulations. - 2012-010

L¹ Error Estimates for Difference Approximations of Degenerate Convection-Diffusion Equations. - 2012-009

Smooth solutions for a*p*-system of mixed type. - 2012-008

A note on a kinetic formulation of the Euler equations. - 2012-007

Proper entropy conditions for scalar conservation laws with discontinuous flux. - 2012-006

Variational analysis of Nash equilibria for a model of traffic flow. - 2012-005

An integro–differential conservation law arising in a model of granular flow. - 2012-004

Lipschitz semigroup for an integro–differential equation for slow erosion. - 2012-003

Admissibility of weak solutions for the compressible Euler equations, n≥2. - 2012-002

High resolution schemes: total variation stability and its dependence on smoothness parameter. - 2012-001

Source terms versus entropy for environmental waves.

## 2011 Preprints

- 2011-027

Exact Riemann solutions to Euler equations in ducts with discontinuous cross-section. - 2011-026

On decay of periodic entropy solutions to a scalar conservation law. - 2011-025

Singular limits for a parabolic-elliptic regularization of scalar conservation laws. - 2011-024

Modelling and numerical approximation of a 2.5D set of equations for mesoscale atmospheric processes. - 2011-023

A study of a WENO-TVD finite volume scheme for the numerical simulation of atmospheric advective and convective phenomena. - 2011-022

High-order finite volume schemes for layered atmospheric models. - 2011-021

A new model for shallow elastic fluids. - 2011-020

On some deficiencies of the AUFS scheme for Euler flows and possible fixes. - 2011-019

Nonlinear dynamics of magnetohydrodynamic flows of heavy fluid over an arbitrary surface in shallow water approximation. - 2011-018

Quasi-two-layer finite-volume scheme for modeling shallow water flows over an arbitrary bed in the presence of external force. - 2011-017

Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws. - 2011-016

Nash equilibria for a model of traffic flow with several groups of drivers. - 2011-015

On the Rayleigh–Taylor instability for two uniform viscous incompressible flows. - 2011-014

On the Rayleigh–Taylor instability for incompressible, inviscid magnetohydrodynamic flows. - 2011-013

Boundary layers for self-similar viscous approximations of nonlinear hyperbolic systems. - 2011-012

Existence of solutions for degenerate parabolic equations with rough coefficients. - 2011-011

Extensions for systems of conservation laws. - 2011-010

On weak completeness of the set of entropy solutions to a degenerate non-linear parabolic equation. - 2011-009

Pairwise wave interactions in ideal polytropic gases. - 2011-008

An exponential time-differencing method for monotonic relaxation systems. - 2011-007

Well-posedness of a singular balance law. - 2011-006

On multi-dimensional sonic-subsonic flow. - 2011-005

Optima and equilibria for a model of traffic flow. - 2011-004

A Domain Decomposition Method for Semilinear Hyperbolic Systems with Two-scale Relaxations. - 2011-003

Operator splitting for two-dimensional incompressible fluid equations. - 2011-002

Richness or Semi-Hamiltonicity of quasi-linear systems which are not in evolution form. - 2011-001

Singular solutions for nonlinear hyperbolic systems.

## 2010 Preprints

- 2010-025

Front tracing approximations for slow erosion. - 2010-024

Strong traces for entropy solutions of heterogeneous ultra-parabolic equations. - 2010-023

Mixed Systems: ODEs – Balance Laws. - 2010-022

Well-posedness for multidimensional scalar conservation law with discontinuous flux. - 2010-021

Finite volume schemes for the approximation via characteristics of linear convection equations with irregular data. - 2010-020

Formation of singularity and smooth wave propagation for the non-isentropic compressible Euler equations. - 2010-019

Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations. - 2010-018

On the origin of divergence errors in MHD simulations and consequences for numerical schemes. - 2010-017

Erosion profile by a global model for granular flow. - 2010-016

Accuracy of the adaptive GRP scheme and the simulation of 2-D Riemann problems for compressible Euler equations. - 2010-015

L^{∞}solutions for a model of polytropic gas flow with diffusive entropy. - 2010-014

An energy-momentum interaction of fluid elements. - 2010-013

Weak entropy solutions of nonlinear reaction-hyperbolic systems for axonal transport. - 2010-012

A uniqueness criterion for viscous limits of boundary Riemann problems. - 2010-011

A generalization ofH -measures and application on purely fractional scalar conservation laws. - 2010-010

A strongly degenerate parabolic aggregation equation. - 2010-009

On the coupling of systems of hyperbolic conservation laws with ordinary differential equations. - 2010-008

Lipschitz metric for the periodic Camassa–Holm equation. - 2010-007

A theory of*L*^{1}-dissipative solvers for scalar conservation laws with discontinuous flux. - 2010-006

A discontinuous Galerkin method for ideal two-fluid plasma equations. - 2010-005

Hamilton Jacobi equations with obstacles. - 2010-004

SBV Regularity for Hamilton–Jacobi Equations in**R**^{n}. - 2010-003

2×2 Systems of Conservation Laws with L^{∞}data. - 2010-002

A unified gas-kinetic scheme for continuum and rarefied flows. - 2010-001

Ultraparabolic*H*-measures and compensated compactness.

## 2009 Preprints

- 2009-060

A blow-up criterion in terms of the density for compressible viscous flows. - 2009-059

Monotone difference schemes stabilized by discrete mollification for strongly degenerate parabolic equations. - 2009-058

Second-order schemes for conservation laws with discontinuous flux modelling clarifier-thickener units. - 2009-057

Global existence and regularity of the weakly compressible Navier–Stokes system. - 2009-056

On vanishing viscosity approximation of conservation laws with discontinuous flux. - 2009-055

Wave propagation in multicomponent flow models. - 2009-054

Modeling the Dynamics of Granular Matter. - 2009-053

A convergent mixed method for the Stokes approximation of viscous compressible flow. - 2009-052

Global semigroup of conservative solutions of the nonlinear variational wave equation. - 2009-051

Strong compactness of approximate solutions to degenerate elliptic-hyperbolic equations with discontinuous flux function. - 2009-050

The computation of nonclassical shock waves with a heterogeneous multiscale method. - 2009-049

Convergence of the space-time expansion discontinuous Galerkin method for scalar conservation laws. - 2009-048

Non-uniqueness of weak solutions for the fractal Burgers equation. - 2009-047

A note on uniqueness of entropy solutions to degenerate parabolic equations in**R**^{N}. - 2009-046

Error bound between monotone difference schemes and their modified equations. - 2009-045

On the compactness for two dimensional scalar conservation law with discontinuous flux. - 2009-044

A note on the new Glimm functional for general systems of hyperbolic conservation laws. - 2009-043

Hierarchical reconstruction with up to second degree remainder for solving nonlinear conservation laws. - 2009-042

Invariant manifolds for a singular ordinary differential equation. - 2009-041

A connection between viscous profiles and singular ODEs. - 2009-040

A high-order gas-kinetic navier-stokes solver I: One-dimensional flux evaluation. - 2009-039

On an optimal number of time steps for a sequential solution of an elliptic–hyperbolic system. - 2009-038

Operator splitting for the KdV equation. - 2009-037

The Kolmogorov–Riesz compactness theorem. - 2009-036

1D compressible flow with temperature dependent transport coefficients. - 2009-035

A convergent nonconforming finite element method for compressible Stokes flow. - 2009-034

The linear appearance theorem for a class of non linear non homogeneous hyperbolic systems involving a transport equation. - 2009-033

A robust well-balanced scheme for multi-layer shallow water equations. - 2009-032

A subsonic-well-balanced reconstruction scheme for shallow water flows. - 2009-031

A blow-up criterion for compressible viscous heat-conductive flows. - 2009-030

Difference-quadrature schemes for nonlinear degenerate parabolic integro-PDE. - 2009-029

The discontinuous Galerkin method for fractal conservation laws. - 2009-028

Vanishing viscosity with short wave long wave interactions for systems of conservation laws. - 2009-027

Existence and Uniqueness for Multidimensional Scalar Conservation Law with Discontinuous Flux. - 2009-026

Homogenization of Nonlinear PDE's in the Fourier–Stieltjes Algebras. - 2009-025

Acoustic limit of the Boltzmann equation: Classical solutions. - 2009-024

Remarks on the acoustic limit for the Boltzmann equation. - 2009-023

Weakly Nonlinear-Dissipative Approximations of Hyperbolic-Parabolic Systems with Entropy. - 2009-022

Lipschitz metric for the Hunter–Saxton equation. - 2009-021

Systems of hyperbolic conservation laws with prescribed eigencurves. - 2009-020

Dilatation of a one-dimensional nonlinear crack impacted by a periodic elastic wave. - 2009-019

Ultra-parabolic equations with rough coefficients. Entropy solutions and strong pre-compactness property. - 2009-018

Singularly perturbed ODEs and profiles for stationary symmetric Euler and Navier–Stokes shocks. - 2009-017

On a stochastic first order hyperbolic equation in a bounded domain. - 2009-016

Convergence of a mixed method for a semi-stationary compressible Stokes system. - 2009-015

Some new well-posedness results for continuity and transport equations, and applications to the chromatography system. - 2009-014

Zero diffusion-dispersion-smoothing limits for scalar conservation law with discontinuous flux function. - 2009-013

New entropy conditions for the scalar conservation law with discontinuous flux. - 2009-012

Sharp convergence rate of the Glimm scheme for general nonlinear hyperbolic systems. - 2009-010

Finite volume schemes for locally constrained conservation laws. - 2009-009

Extended Gas Dynamic Equations for Microflows. - 2009-008

Asymptotic behavior of global classical solutions to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small BV data. - 2009-007

Stability of entropy solutions for Lévy mixed hyperbolic-parabolic equations. - 2009-006

Leray weak solutions of the Incompressible Navier Stokes system on exterior domains via the artificial compressibility method. - 2009-005

Large time decay of solutions to isentropic gas dynamics with spherical symmetry. - 2009-004

Numerical methods for river flow modelling. - 2009-003

The Slow Erosion Limit in a Model of Granular Flow. - 2009-002

Symmetric Hyperbolic Equations of Motion for a Hyperelastic Material. - 2009-001

Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations.

## 2008 Preprints

- 2008-041

Regularity of entropy solutions. - 2008-040

A positive MUSCL–Hancock scheme for ideal magnetohydrodynamics. - 2008-039

Convergent finite element methods for compressible barotropic Stokes systems. - 2008-038

Front tracking for a model of immiscible gas flow with large data. - 2008-037

Global*L*^{∞}solutions of the compressible Euler Equations with spherical symmetry. - 2008-036

Initial-boundary value problems for conservation laws with source terms and the Degasperis–Procesi equation. - 2008-035

A Liapunov-Schmidt Reduction for Time-Periodic Solutions of the Compressible Euler Equations. - 2008-034

Time-Periodic Linearized Solutions of the Compressible Euler Equations and a Problem of Small Divisors. - 2008-033

A Paradigm for Time-Periodic Sound Wave Propagation in the Compressible Euler Equations. - 2008-032

Global Wave Interactions in Isentropic Gas Dynamics. - 2008-031

Well-posedness results for triply nonlinear degenerate parabolic equations. - 2008-030

Regularity and Global Structure of Solutions to Hamilton–Jacobi equations II. Convex initial data. - 2008-029

3-D kinematical Conservation Laws: Equations of Evolution of a Surface. - 2008-028

A Central Rankine Hugoniot Solver for Hyperbolic Conservation Laws. - 2008-027

On a strong precompactness of velocity averages for a heterogenous transport equation with rough coefficients. - 2008-026

Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions. - 2008-025

An application of 3-D kinematical conservation laws: Propagation of a three dimensional wavefront. - 2008-024

An exactly conservative particle method for one dimensional scalar conservation laws. - 2008-023

Global Existence of Large BV Solutions in a Model of Granular Flow. - 2008-022

On the strong pre-compactness property for entropy solutions of an ultra-parabolic equation with discontinuous flux. - 2008-021

Asymptotics toward rarefaction waves and vacuum for 1-d Compressible Navier–Stokes equations. - 2008-020

A convergence result for finite volume schemes on 2-dimensional Riemannian manifolds. - 2008-019

A mathematical model for tsunami generation using a conservative velocity-pressure hyperbolic system. - 2008-018

A multiwave approximate Riemann solver for ideal MHD based on relaxation II – Numerical implementation with 3 and 5 waves. - 2008-017

On weak convergence of entropy solutions to scalar conservation laws. - 2008-016

On existence and uniqueness of entropy solutions to the Cauchy problem for a conservation law with discontinuous flux. - 2008-015

A New Glimm Functional and Convergence Rate of Glimm Scheme for General Systems of Hyperbolic Conservation Laws. - 2008-014

Compressible 1-D Euler Equations with Large Data: A Case Study. - 2008-013

Symmetric Euler and Navier–Stokes shocks in stationary barotropic flow on a bounded domain. - 2008-012

Dissipative solutions for the Camassa–Holm equation. - 2008-011

Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process. - 2008-010

Sound traveling-waves in wind instruments as solutions to non linear non homogeneous gas dynamics equations. - 2008-009

Structure of fundamental solutions of a conservation law without convexity. - 2008-008

Spectral stability of weak relaxation shock profiles. - 2008-007
:

Dynamics of the density discontinuity interface. A transversal contact problem. - 2008-006
:

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
:

Solving one dimensional scalar conservation laws by particle management. - 2008-001
:

A uniqueness condition for non-linear convection-diffusion equations with discontinuous coefficients.

## 2007 Preprints

- 2007-032
:

Singular solutions to systems of conservation laws: shocks, δ- and δ'-shocks. - 2007-031
:

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
:

The solution of the Cauchy problem with large data for a model of a mixture of gases. - 2007-026
:

Hyperbolic Conservation Laws with Discontinuous Fluxes and Hydrodynamic Limit for Particle Systems. - 2007-025
:

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
:

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
:

Mach-uniform accuracy and efficiency of a semi-implicit/explicit algorithm to solve compressible Euler equations for general fluids. - 2007-016
:

A convergent finite difference method for a nonlinear variational wave equation. - 2007-015
:

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
:

Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations. - 2007-011
:

An Engquist–Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections. - 2007-010
:

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
:

Stability of Viscous Shocks on Finite Intervalls. - 2007-007
:

High Order Well-balanced Finite Volume WENO Schemes for Shallow Water Equation with Moving Water. - 2007-006
:

Gearhart–Prüss Theorem and linear stability for Riemann solutions of conservation laws. - 2007-005
:

Critical thresholds in a relaxation model for travel flows. - 2007-004
:

A Field Space-based Level set Method for Computing Multi-valued Solutions. - 2007-003
:

On the existence and compactness of a two-dimensional resonant system of conservation laws. - 2007-002
:

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
:

A Model Problem for the Motion of a Compressible, Viscous Fluid Flow with the No-Slip Boundary Condition. - 2006-057
:

Delta shock wave formation in the case of triangular hyperbolic system of conservation laws. - 2006-056
:

On the Delta-Shock Front Problem. - 2006-055
:

Numerical comparison of Riemann solvers for astrophysical hydrodynamics. - 2006-054
:

On the Shape of Avalanches. - 2006-053
:

On delta-shocks and singular shocks. - 2006-052
:

Godunov scheme and sampling technique for computing phase transitions in traffic flow modeling. - 2006-051
:

Transport-Equilibrium Schemes for Computing Nonclassical Shocks. Scalar Conservation Laws. - 2006-050
:

On the Comparison of Evolution Galerkin and Discontinuous Galerkin Schemes. - 2006-049
:

Vanishing Viscosity Approximation to Hyperbolic Conservation Laws. - 2006-048
:

Convergence rate of monotone numerical schemes for Hamilton-Jacobi equations with weak boundary conditions. - 2006-047
:

Systems of Hyperbolic Conservation Laws with Memory. - 2006-046
:

Well-Balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation. - 2006-045
:

Existence of strong traces for quasi-solutions of multidimensional scalar conservation laws. - 2006-044
:

Interaction of Rarefaction Waves of the Two-Dimensional Self-Similar Euler Equations. - 2006-043
:

A multiwave approximate Riemann solver for ideal MHD based on relaxation I – Theoretical framework. - 2006-042
:

Effective Thermoviscoelasticity of a Saturated Porous Ground. - 2006-041
:

On singularities of conservation equation solution. (Updated 2006-11-10.) - 2006-040
:

A family of schemes for kinematic flows with discontinuous flux. - 2006-039
:

Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes. - 2006-038
:

A convergent finite difference scheme for the Camassa–Holm equation with general*H*^{1}initial data. - 2006-035
:

Periodic conservative solutions of the Camassa–Holm equation. - 2006-034
:

*L*^{2}formulation of multidimensional scalar conservation laws. - 2006-033
:

Remarks on vacuum state and uniqueness of concentration process. - 2006-032
:

On the global regularity of sub-critical Euler–Poisson equations with pressure. - 2006-031
:

On the piecewise smoothness of entropy solutions to scalar conservation laws for a large class of initial data. - 2006-030
:

A second-order BGK scheme for the equations of radiation hydrodynamics. - 2006-029
:

Central Discontinuous Galerkin Methods on Overlapping Cells with a Non-Oscillatory Hierarchical Reconstruction. - 2006-028
:

A dispersive approach to the artificial compressibility approximations of the Navier Stokes equations in 3-D. - 2006-027
:

Dependence of Entropy Solutions in the Large for the Euler Equations on Nonlinear Flux Functions. - 2006-026
:

Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem. - 2006-025
:

On Two-Dimensional Sonic-Subsonic Flow. - 2006-024
:

Slow eigenvalues of self-similar solutions of the Dafermos regularization of a system of conservation laws: An analytic approach. - 2006-023
:

Global Dissipative Solutions of the Camassa–Holm Equation. - 2006-022
:

Optimality Conditions for Solutions to Hyperbolic Balance Laws. - 2006-021
:

The boundary Riemann solver coming from the real vanishing viscosity approximation. - 2006-020
:

Analytic Semigroup Generated by the Linearization of a Riemann–Dafermos Solution. - 2006-019
:

*L*^{2}semigroup and linear stability for Riemann solutions of conservation laws. - 2006-018
:

Global conservative solutions of the generalized hyperelastic-rod wave equation. - 2006-017
:

Convergence of finite volume schemes for triangular systems of conservation laws. - 2006-016
:

Uniqueness and Sharp Estimates on Solutions to Hyperbolic Systems with Dissipative Source. - 2006-015
:

Solutions for a Nonlocal Conservation Law with Fading Memory. - 2006-014
:

Global Solutions of Shock Reflection by Large-Angle Wedges for Potential Flow. - 2006-013
:

Numerical schemes for computing discontinuous solutions of the Degasperis–Procesi equation. - 2006-012
:

Local existence and finite-time blow-up in multidimensional radiation hydrodynamics. - 2006-011
:

Global conservative multipeakon solutions of the Camassa-Holm equation. - 2006-010
:

A Hamiltonian-preserving scheme for high frequency elastic waves in heterogeneous media. - 2006-009
:

Existence and stability of curved multidimensional detonation fronts. - 2006-008
:

Numerical investigation of cavitation in multi-dimensional compressible flows. - 2006-007
:

Shock profiles for non-equilibrium radiating gases. - 2006-006
:

Vanishing viscosity limit to rarefaction waves for the Navier-Stokes equations of one-dimensional compressible heat-conducting fluids. - 2006-005
:

On the relations between uniqueness for the Cauchy problem and existence of smooth approximations for linear transport equations. - 2006-004
:

On the uniqueness of discontinuous solutions to the Degasperis-Procesi equation. - 2006-003
:

Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws. - 2006-002
:

Characteristic parameters of a wide cluster in a higher-order traffic flow. - 2006-001
:

Global conservative solutions of the Camassa-Holm equation - a Lagrangian point of view.

## 2005 Preprints

- 2005-055
:

On the algebraic aspect of singular solutions to conservation laws systems. - 2005-054
:

Fractional and fractal derivatives modeling of turbulence. - 2005-053
:

The Riemann problem admitting δ′-shock wave type solution (the vanishing viscosity approach). - 2005-052
:

The Aw–Rascle traffic flow model with phase transitions. - 2005-051
:

On symmetrizability of hyperbolic matrix spaces. - 2005-050
:

Prolonged systems for a scalar conservation law and entropies of higher order. - 2005-049
:

On infinite dimensional systems of conservation laws of Keyfitz-Kranzer type. - 2005-048
:

A Mathematical model for rogue waves, using Saint Venant equations with friction. - 2005-047
:

Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy. - 2005-046
:

Non-oscillatory central schemes for one- and two-dimensional MHD equations. II: high-order semi-discrete schemes. - 2005-045
:

Compensated compactness for 2D conservation laws. - 2005-044
:

Velocity averaging, kinetic formulations and regularizing effects in quasilinear PDEs. - 2005-043
:

A Lagrangian central scheme for interface problems. - 2005-042
:

Upwinding of source term at interfaces for Euler equations with high friction. - 2005-041
:

New scenario for transition to slow 3-D turbulence. - 2005-040
:

H^{1}-perturbations of smooth solutions for a weakly dissipative hyperelastic-rod wave equation. - 2005-039
:

Optimal tracing of viscous shocks in solutions of viscous conservation laws. - 2005-038
:

Modeling 1-D elastic P-waves in a fractured rock with hyperbolic jump conditions. - 2005-037
:

A note on the shock wave formation process for scalar conservation laws. - 2005-036
:

Explicit solutions of a convection-reaction equation and defects of difference schemes. - 2005-035
:

Simple waves and a characteristic decomposition of the two dimensional compressible Euler equations. - 2005-034
:

Convergent difference schemes for the Hunter–Saxton equation. - 2005-033
:

On a lemma Of DiPerna And Chen. - 2005-032
:

Vanishing viscosity solutions of a 2×2 triangular hyperbolic system with Dirichlet conditions on two boundaries. - 2005-031
:

A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway. - 2005-030
:

Hyperbolicity and kinematic waves of a class of multi-population partial differential equations. - 2005-029
:

Helically symmetric solutions to the 3-D Navier-Stokes equations for compressible isentropic fluids. - 2005-028
:

On the well-posedness of the Degasperis-Procesi equation. - 2005-027
:

Well-balanced finite volume evolution Galerkin methods for the shallow water equations. - 2005-026
:

Finite difference schemes with cross derivatives correctors for multidimensional parabolic systems. - 2005-025
:

A direct Eulerian GRP scheme for compressible fluid flows. - 2005-024
:

Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with transmissions and reflections. - 2005-023
:

Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds. - 2005-022
:

Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials. - 2005-021
:

Visual simulation of shallow-water waves. - 2005-020
:

Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows. - 2005-019
:

The nonrelativistic limit in radiation hydrodynamics: I. Weak entropy solutions for a model problem. - 2005-018
:

An optimal transportation metric for solutions of the Camassa-Holm equation. - 2005-017
:

A singular limit problem for conservation laws related to the Camassa–Holm shallow water equation. - 2005-016
:

Global conservative solutions of the Camassa–Holm equation. - 2005-015
:

Stability of finite difference schemes for hyperbolic systems in two space dimensions. - 2005-014
:

Pointwise asymptotic behavior of perturbed viscous shock profiles. - 2005-013
:

On the convergence of SPH method for scalar conservation laws with boundary conditions. - 2005-012
:

δ^{n}-shock wave as a new type solutions of hyperbolic systems of conservation laws. - 2005-011
:

Two-dimensional regular shock reflection for the pressure gradient system of conservation laws. - 2005-010
:

Conservative Solutions to a Nonlinear Variational Wave Equation. - 2005-009
:

An Instability of the Godunov Scheme. - 2005-008
:

Global weak solutions to a generalized hyperelastic-rod wave equation. - 2005-007
:

Wellposedness for a parabolic-elliptic system. - 2005-006
:

Global solutions of the Hunter–Saxton equation. - 2005-005
:

Wave decomposition in Riemann problems for heterogeneous media. - 2005-004
:

A convergent numerical scheme for the Camassa–Holm equation based on multipeakons. - 2005-003
:

On isentropic solutions of first-order quasilinear equations. - 2005-002
:

On correctness classes of locally bounded generalized entropy solutions to Cauchy problem for first order quasilinear equations. - 2005-001
:

Existence of strong traces for generalized solutions of multidimensional scalar conservation laws.

## 2004 Preprints

- 2004-074
:

Symmetries and global solvability of the isothermal gas dynamics equations. - 2004-073
:

Nonclassical Riemann solvers with nucleation. - 2004-072
:

On the validity of the Chapman-Enskog expansion for shock waves with small strength. - 2004-071
:

Front motion in viscous conservation laws with stiff source terms. - 2004-070
:

Relative entropy in hyperbolic relaxation. - 2004-069
:

Existence and stability of multidimensional transonic flows through an infinite nozzle of arbitrary cross-sections. - 2004-068
:

A non standard free-boundary problem arising from stratigraphy. - 2004-067
:

On the approximation of the non-autonomous nonlinear Riemann problem. - 2004-066
:

Hydrodynamic limits for kinetic equations and the diffusive approximation of radiative transport for acoustic waves. - 2004-065
:

Structural properties of stress relaxation and convergence from viscoelasticity to polyconvex elastodynamics. - 2004-064
:

Central Runge-Kutta schemes for hyperbolic conservation laws. - 2004-063
:

Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. - 2004-062
:

The strong relaxation limit of the multidimensional isothermal Euler equations. - 2004-061
:

Hyperbolic-elliptic systems of conservation laws. - 2004-060
:

Hyperbolic limit of the Jin–Xin relaxation model. - 2004-059
:

Delta-shocks, the Rankine–Hugoniot conditions, and singular superposition of distributions. - 2004-058
:

A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. - 2004-057
:

A Note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations. - 2004-056
:

Blow-up of the BV norm in the multidimensional Keyfitz and Kranzer system. - 2004-055
:

Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions. - 2004-054
:

Minimal entropy conditions for Burgers equations. - 2004-053
:

Concentration estimates for entropy measures. - 2004-052
:

Existence of solutions for a class of hyperbolic systems of conservations laws in several space dimensions. - 2004-051
:

Structure of entropy solutions to the Eikonal equation. - 2004-050
:

Structure of entropy solutions for multi-dimensional conservation laws. - 2004-049
:

On the optimality of velocity averaging lemmas. - 2004-048
:

Asymptotic behavior of spatially inhomogeneous balance laws. - 2004-047
:

Error bounds for monotone approximation schemes for Hamilton–Jacobi–Bellman equations. - 2004-046
:

On error bounds for monotone approximation schemes for multi-dimensional Isaacs equations. - 2004-045
:

Source waves. - 2004-044
:

Equivalence of low frequency stability conditions for multidimensional detonations in three models of combustion. - 2004-043
:

Central schemes on overlapping cells. - 2004-042
:

Global solutions to the Boltzmann equation with external forces. - 2004-041
:

Stability of undercompressive shock profiles. - 2004-040
:

phase transitions and sharp-interface limits for the 1d-elasticity system with non-local energy. - 2004-039
:

Instability of Travelling Wave Profiles for the Lax–Friedrichs scheme. - 2004-038
:

Convergence of a finite difference scheme for the Camassa–Holm equation. - 2004-037
:

A front-tracking method for the simulation of three-phase flow in porous media. - 2004-036
:

Continuous dependence estimates for viscosity solutions of integro-PDEs. - 2004-035
:

A bi-hyperbolic finite volume method on quadrilateral meshes. - 2004-034
:

Order preserving vibrating strings and applications to electrodynamics and magnetohydrodynamics. - 2004-033
:

Remarks on the formation and decay of multidimensional shock waves. - 2004-032
:

On the Riemann Problem for a Hyperbolic Two-Phase Flow Model. - 2004-031
:

Uniqueness of entropy solutions for doubly nonlinear anisotropic degenerate parabolic equations. - 2004-030
:

Stability of large-amplitude shock profiles of general relaxation systems. - 2004-029
:

Nonlinear operator integration factor splitting for the shallow water equations. - 2004-028
:

Propagation of curved shock fronts using shock ray theory and comparison with other theories. - 2004-027
:

Cauchy problem for the Vlasov-Poisson-Boltzmann system. - 2004-026
:

A half-space problem for the Boltzmann equation with specular reflection boundary condition. - 2004-025
:

Burgers' equation with vanishing hyper-viscosity. - 2004-024
:

Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient. - 2004-023
:

Divergence-measure fields, sets of finite perimeter, and conservation laws. - 2004-022
:

A high order kinetic flux-splitting method for the relativistic magnetohydrodynamics. - 2004-021
:

A high order kinetic flux-splitting method for the special relativistic hydrodynamics. - 2004-020
:

On asymptotic variational wave equations. - 2004-019
:

The genuinely nonlinear non-isotropic ultra-parabolic equation. - 2004-018
:

Nearly Lipshitzean divergence free transport does not propagate continuity and BV regularity. - 2004-017
:

Uniqueness and nonuniquess for nonsmooth divergence free transport. - 2004-016
:

C^{1}measure respecting maps preserve bv iff they have bounded derivative. - 2004-015
:

Rotating fluids with self-gravitation in bounded domains. - 2004-014
:

A mathematical model for hurricanes. - 2004-013
:

A second-order γ-model BGK scheme for multimaterial compressible flows. - 2004-012
:

Gradient driven and singular flux blowup of smooth solutions to hyperbolic conservation laws. - 2004-011
:

Global structure and asymptotic behavior of weak solutions to flood wave equations. - 2004-010
:

Well-posedness for a scalar conservation law with singular non-conservative source. - 2004-009
:

Well-posedness of hyperbolic initial boundary value problems. - 2004-008
:

On large time step Godunov scheme for hyperbolic conservation laws. - 2004-007
:

On the well posedness for hyperbolic systems of conservation laws with large*BV*data. - 2004-006
:

Application of the method of kinetic equation to the Darcy–Stefan problem. - 2004-005
:

Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux. - 2004-004
:

Continuous Glimm-type functionals and spreading of rarefaction waves. - 2004-003
:

L^1-framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations. - 2004-002
:

On isentropic solutions to first order quasilinear equations. - 2004-001
:

Some results on general system of isentropic gas dynamics.

## 2003 Preprints

- 2003-078
:

Weak asymptici of shock wave formation process. - 2003-077
:

Convergence of upwind finite difference algorithms for scalar conservation laws with indefinite discontinuitites in the flux function. - 2003-076
:

Perturbation of singular equilibria of hyperbolic two-component systems: a universal hydrodynamic limit. - 2003-075
:

Derivation of the Leroux system as the hydrodynamic limit of a two-component lattice gas. - 2003-074
:

Onsager relations and Eulerian hydrodynamic limit for systems with several conservation laws. - 2003-073
:

A mixture flux approach for accurate and robust resolution of two-phase flows. - 2003-072
:

Weakly implicit numerical schemes for the two-fluid model. - 2003-071
:

CFL-free numerical schemes for the two-fluid model. - 2003-070
:

Comparison of various AUSM type schemes for the two-fluid model. - 2003-069
:

Semi-cooperative strategies for differential games. - 2003-068
:

dynamics of propagation and interaction of delta-shock waves in conservation law systems. - 2003-067
:

Low Frequency Stability of Multi-dimensional Inviscid Planar Detonation Waves. - 2003-066
:

Existence of global entropy solutions to Euler equations of compressible fluid flow. - 2003-065
:

Composite waves in the Dafermos regularization. - 2003-064
:

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces. - 2003-063
:

Initial boundary value problems for a quasilinear parabolic system in three-phase capillary flow in porous media. - 2003-062
:

Non-oscillatory central schemes for one- and two-dimensional MHD equations. I. - 2003-061
:

Numerical comparison of the method of transport to a standard scheme. - 2003-060
:

On the connection between some Riemann-Solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws. - 2003-059
:

A specific hyperbolic system of conservation laws admitting delta-shock wave type solutions. - 2003-058
:

Stability of large-amplitude shock profiles for general relazation systems. - 2003-057
:

Stability of large-amplitude viscous shock profiles of hyperbolic-parabolic systems. - 2003-056
:

Control problems for systems of conservation law. - 2003-055
:

PDE fluid modeling of multithread systems and optimal control. - 2003-054
:

Symmetric nonbarotropic flows with large data and forces. - 2003-053
:

Spatially periodic solutions in relativistic isentropic gas dynamics. - 2003-052
:

Delta-shock wave type solution of hyperbolic systems of conservation laws. - 2003-051
:

Existence of Dafermos profiles for singular shocks. - 2003-050
:

A five equation reduced model for compressible two phase flow problems. - 2003-049
:

Neumann boundary conditions for Hamliton Jacobi equations in a quarter plane. - 2003-048
:

On the problem of symmetrizability for hyperbolic systems of first order. - 2003-047
:

On evolution Galerkin methods for the Maxwell and the linearized Euler equations. - 2003-046
:

On the boundary conditions for EG-methods applied to the two-dimensional wave equation system. - 2003-045
:

Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system. - 2003-044
:

A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. - 2003-043
:

Second-order Godunov-type scheme for reactive flow calculations on moving meshes. - 2003-042
:

On the convergence rate of vanishing viscosity approximations. - 2003-041
:

Stability of solutions of quasilinear parabolic equations. - 2003-040
:

A "maximum principle for semicontinuous functions" applicable to integro-partial differential equations. - 2003-039
:

Renormalized entropy solutions for quasilinear anisotropic degenerate parabolic equations. - 2003-038
:

Asymptotic stability of non-planar Riemann solutions for a special class of multi-d systems of conservation laws. - 2003-037
:

Scalar conservation laws with boundary conditions and rough data measure solutions. - 2003-036
:

A class of high resolution schemes for hyperbolic conservation laws and convection–diffusion equations with varying time and space grids. - 2003-035
:

A note on (2k+1)-point conservative monotone schemes. - 2003-034
:

A class of high resolution difference schemes for nonlinear Hamilton-Jacobi equations with varying time and space grids. - 2003-033
:

Stability conditions for strong rarefaction waves - 2003-032
:

Lyapunov functional for solutions of systems of conservation laws containing a strong rarefaction. - 2003-031
:

A moving mesh method for the Euler flow calculations using a directional monitor function. - 2003-030
:

A sharp decay estimate for positive nonlinear waves. - 2003-029
:

MOCL - An algorithm for tracking interfaces in two-dimensional Eulerian codes. - 2003-028
:

Hydrodynamic structure of the augmented Born-Infeld equations. - 2003-027
:

Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice; I. Homogeneous problems; vanishing exterior potentials. - 2003-026
:

Numerical simulation of compressible two-phase flow model based on the Riemann problem. - 2003-025
:

A level set method for the computation of multivalued solutions to quasi-linear hyperbolic PDEs and Hamilton-Jacobi equations. - 2003-024
:

On the global stability of contact discontinuity for compressible Navier-Stokes equations. - 2003-023
:

Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients. - 2003-022
:

*L*^{1}stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. - 2003-021
:

Small BV solutions of hyperbolic non-cooperative differential games. - 2003-020
:

The stability of compressible vortex sheets in two space dimensions. - 2003-019
:

On the solution to the Riemann problem for the compressible duct flow. - 2003-018
:

On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary. - 2003-017
:

Front tracking for scalar balance equations. - 2003-016
:

A reduction of the Boltzmann-Peierls equation. - 2003-015
:

Godunov-type approximation for a general resonant balance law with large data. - 2003-014
:

A lemma and a conjecture on the cost of rearrangements. - 2003-013
:

An ill posed Cauchy problem for a hyperbolic system in two space dimensions. - 2003-012
:

Stable and accurate hybrid finite volume methods based on pure convexity arguments for hyperbolic systems of conservation law. - 2003-011
:

On the rate of convergence of approximation schemes for Bellman equations associated with optimal stopping time problems. - 2003-010
:

$W^{2,\infty}$ regularizing effect in a nonlinear, degenerate parabolic equation in one space dimension. - 2003-009
:

Error bounds for monotone approximation schemes for non-convex degenerate elliptic equations in $\mathbb{R}^1$. - 2003-008
:

The Riemann problem for a class of resonant hyperbolic systems of balance laws. - 2003-007
- 2003-006
:

Well-posedness in $BV_t$ and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units. - 2003-005
:

Long time behavior of solutions to the 3D compressible Euler equations with damping. - 2003-004
:

BGK-type kinetic flux vector splitting scheme for the ultra-relativistic Euler equations. - 2003-003
:

An entropy condition and global existence result for hyperbolic balance laws. - 2003-002
:

A Lagrangian discontinous Galerkin type method on unstructured meshes to solve hydrodynamics problems. - 2003-001
:

Some recent methods for partial differential equations of divergence form.

## 2002 Preprints

- 2002-059
:

A practical spectral method for hyperbolic conservation laws. - 2002-058
:

Pointwise Green's function bounds for shock profiles of systems with real viscosity. - 2002-057
:

On the numerical simulation of multiphase flows with changes of phase and strong gradients using the homogeneous equilibrium model. - 2002-056
:

Conservation laws with time dependent discontinuous coefficients. - 2002-055
:

Asymptotic stability of Riemann solutions for a class of multi-d viscous systems of conservation laws. - 2002-054
:

Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy. - 2002-053
:

Finite volume evolution Galerkin (FVEG) methods for hyperbolic systems. - 2002-052
:

Global entropy solutions to exothermically reacting, compressible Euler equations. - 2002-051
:

An antidiffusive entropy scheme for monotone scalar conservation laws. - 2002-050 Not available
- 2002-049
:

On kinetic formulation of measure valued and strong measure valued solutions. - 2002-048
:

The Riemann problem for the Baer-Nunziato model of two-phase flows. - 2002-047
:

Computation of Riemann solutions using the Dafermos regularization and continuation. - 2002-046
:

Central schemes and systems of conservation laws with discontinuous coefficients modeling gravity separation of polydisperse suspensions. - 2002-045
:

Mathematical model and numerical simulation of the liquid fluidization of polydisperse solid particle mixtures. - 2002-044 Removed by request from the authors
- 2002-043
:

On the optimization of a conservation law. - 2002-042
:

Weakly stable multi-d shocks. - 2002-041
:

Global well-posedness and relaxation limits of a model for radiating gas. - 2002-040
:

Kinetic schemes for the relativistic gas dynamics. - 2002-039
:

Kinetic schemes for the ultra-relativistic Euler equations. - 2002-038
:

Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type. - 2002-037
:

Extended divergence-measure fields and the Euler equations for gas dynamics. - 2002-036
:

Convergence of viscosity solutions for isothermal gas dynamics. - 2002-035
:

Weak solution to pressureless type system. - 2002-034
:

A relaxation scheme for conservation laws with a discontinuous coefficient. - 2002-033
:

A gas-solid free boundary problem for compressible viscous gas. - 2002-032
:

Viscous shock wave and boundary layer solution to an inflow problem for compressible viscous gas. - 2002-031
:

Stability of multidimensional undercompressive shock waves. - 2002-030
:

A reduced stability condition for nonlinear relaxation to conservation laws. - 2002-029
:

A discrete BGK approximation for strongly degenerate parabolic problems with boundary conditions. - 2002-028
:

A posteriori error estimate for front-tracking for nonlinear systems of conservation laws. - 2002-027
:

On the attainable set for temple class systems with boundary controls. - 2002-026
:

On a model for continuous sedimentation in vessels with discontinuously varying cross-sectional area. - 2002-025
:

Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression. - 2002-024
:

One sided estimates and uniqueness for hyperbolic systems of balance laws. - 2002-023
:

Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy. - 2002-022
:

H-box methods for the approximation of hyperbolic conservation laws on irregular grids. - 2002-021
:

An adaptive mesh redistribution algorithm for convection-dominated problem. - 2002-020
:

Undercompressive shock waves and the Dafermos regularization. - 2002-019
:

Stability of self-similar solutions of the Dafermos regularization of a system of conservation laws. - 2002-018
:

Evolution galerkin schemes applied to the two-dimensional Riemann problems for the wave equation system. - 2002-017
:

Finite volume evolution Galerkin methods for nonlinear hyperbolic systems. - 2002-016
:

Godunov's scheme and moving adaptive grids. - 2002-015
:

An adaptive mesh redistribution method for nonlinear Hamilton-Jacobi equations in two- and three-dimensions. - 2002-014
:

Nonlinear stability of suliciu model for dynamic phase transitions. - 2002-013
:

Evaluation of the lopatinski determinant for multi-dimensional Euler equations. - 2002-012
:

Traffic flow on a road network. - 2002-011
:

Kinetic approximation of a boundary value problem for conservation laws. - 2002-010
:

Service time assessment in Computational Information Fluid Dynamics using level set methods. - 2002-009
:

Feasibility of fluid transport modelling for buffer and processing systems : Information Fluid Dynamics. - 2002-008
:

Remarks on weak solutions to the Navier-Stokes equations for 2-D comprssible isothermal fluids with spherically symmetric initial data. - 2002-007
:

Shock capturing by anisotropic diffusion oscillation reduction. - 2002-006
:

A wave propagation method for conservation laws and balance laws with spatially varying flux functions. - 2002-005
:

Several applications of generalized solutions in some examples of wave propagation. - 2002-004
:

Weak solutions for a hyperbolic system with unilateral constraint and mass loss. - 2002-003
:

A class of the relaxation schemes for two-dimensional Euler systems of gas dynamics. - 2002-002
:

On a free boundary problem for a strongly degenerate quasilinear parabolic equation with an application to a model of pressure filtration. - 2002-001
:

The Cauchy problem for the Euler equations for compressible fluids.

## 2001 Preprints

- 2001-053
:

Discrete cell entropy inequalities for scalar conservation laws. - 2001-052
:

High resolution conjugate filters for the simulation of flows. - 2001-051
:

Spectral dynamics of the velocity gradient field in restricted flows. - 2001-050
:

Vanishing viscosity solutions of nonlinear hyperbolic systems. - 2001-049
:

Comparison of several difference schemes on 1D and 2D test problems for the Euler equations. - 2001-048
:

Weak stability of non uniformly stable multidimensional shocks. - 2001-047
:

On maximal and minimal generalized entropy solutions to Cauchy problem for a first-order quasilinear equation. - 2001-046
:

Decay of positive waves for $n \times n$ hyperbolic systems of balance laws. - 2001-045
:

A nonconservative numerical approach for hyperbolic systems with source terms: the Well-Balanced schemes. - 2001-044
:

Shock-capturing with natural high frequency oscillations. - 2001-043
:

Application of moving adaptive grids for numerical solution of 2-d nonstationary problems in gas dynamics. - 2001-042
:

Variational barrier method of adaptive grid generation in hyperbolic problem of gas dynamics. - 2001-041
:

A mathematical model for batch and continuous thickening of flocculent suspensions in vessels with varying cross section. - 2001-040
:

Numerical methods for the simulation of continuous sedimentation in ideal clarifier-thickener units. - 2001-039
:

A moving mesh finite element algorithm for singular problems in two and three space dimensions. - 2001-038
:

Fractional rate of convergence for viscous approximation tononconvex conservation laws. - 2001-037
:

Higher-order relaxation schemes for hyperbolic systems of conservation laws. - 2001-036
:

Some traffic flow models illustrating interesting hyperbolic behavior. - 2001-035
:

Finite volume methods for nonlinear elasticity in heterogeneous media. - 2001-034
:

On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations. - 2001-033
:

On the boundary control of systems of conservation laws. - 2001-032
:

On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. - 2001-031
:

An improved quadrature rule for the flux-computation in staggered central difference schemes in multidimensions. - 2001-030
:

A simple method for compressible multiphase mixtures and interfaces. - 2001-029
:

Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations. - 2001-028
:

Asymptotic stability of traveling waves for viscous conservation laws with dissipation. - 2001-027
:

Pointwise Green's function bounds and stability of relaxation shocks. - 2001-026
:

Well posedness for pressureless flow. - 2001-025
:

Generalized characteristics and the uniqueness of entropy solutions to zero-pressure gas dynamics. - 2001-024
:

Error bounds for the large time step Glimm scheme applied to scalar conservation laws. - 2001-023
:

Existence and uniqueness of solutions for a non-uniformly parabolic equation. - 2001-022
:

Convergence of an upwind difference scheme for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. - 2001-021
:

A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units. - 2001-020
:

On the nonhamilton character of shocks in 2-D pressureless gas. - 2001-019
:

Model equations and instability regions for the sedimentation of polydisperse suspensions of spheres. - 2001-018
:

A well-balanced gas-kinetic scheme for the shallow water equations with source terms. - 2001-017
:

Localization effects and measure source terms in numerical schemes for balance laws. - 2001-016
:

On the piecewisely smooth solutions to non-homogeneous scalar conservation laws. - 2001-015
:

Front motion in muti-dimensional conservation laws with stiff source terms driven by mean curvature and variation of front thickness. - 2001-014
:

Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws. - 2001-013
:

On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient. - 2001-012
:

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
:

A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method. - 2001-010
:

Numerical entropy production for central schemes. - 2001-009
:

A priori and a posteriori error estimates for the staggered Lax-Friedrichs scheme in multi-dimensions for scalar nonlinear conservation laws. - 2001-008
:

An error estimate for viscous approximate solutions of degenerate parabolic equations. - 2001-007
:

Stability and convergence of discrete kinetic approximations to an initial-boundary value problem for conservation laws. - 2001-006
:

Blowup in $L^{\infty}$ for a class of genuinely nonlinear hyperbolic systems of conservation laws. - 2001-005
:

Axisymmetric solutions of the 3-D Navier-Stokes equations for compressible isentropic fluids. - 2001-004
:

Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations. - 2001-003
:

A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations. - 2001-002
:

A class of approximate Riemann solvers and their relation to relaxation schemes. - 2001-001
:

TVD schemes for two-dimensional scalar conservation laws.

## 2000 Preprints

- 2000-050
:

Global BV entropy solutions and uniqueness for hyperbolic systems of balance laws. - 2000-049
:

High resolution nonoscillatory central difference schemes for the 2D Euler equations via artificial compression. - 2000-048
:

Uniqueness and stability of $l^\infty$ solutions for Temple class systems with boundary and properties of the attainable sets. - 2000-047
:

Nonhomogeneous Dirichlet problems for degenerate parabolic-hyperbolic equations. - 2000-046
:

Diffusive kinetic explicit schemes for nonlinear degenerate parabolic systems. - 2000-045
:

Convergence of singular limits for multi-d semilinear hyperbolic systems to parabolic systems. - 2000-044
:

A BGK approximation to nonlinear parabolic initial-boundary value problems. - 2000-043
:

Global existence of weak solution for a nonstrictly hyperbolic system of conservation laws. - 2000-042
:

Entropy satisfying flux vector splittings and kinetic BGK models. - 2000-041
:

Phenomenological model of filtration processes: 1. Cake formation and expression. - 2000-040
:

Finite-difference quasi-P traveltimes for anisotropic media. - 2000-039
:

An adaptive finite-difference method for traveltimes and amplitudes. - 2000-038
:

A case study in vanishing viscosity. - 2000-037
:

Solution of two-dimensional Riemann problems for gas dynamics. - 2000-036
:

On the stability of the standard Riemann semigroup. - 2000-035
:

Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients. - 2000-034
:

Convergence results for an inhomogeneous system arising in various high frequency approximations. - 2000-033
:

A wave front tracking algorithm for NxN non genuinely nonlinear conservation laws. - 2000-032
:

Convergence of diffusive BGK approximations for nonlinear strongly parabolic systems. - 2000-031
:

Numerical solution of reservoir flow models based on large time step operator splitting algorithms. - 2000-030
:

A difference scheme for conservation laws with a discontinuous flux - the nonconvex case. - 2000-029
:

Generation of new solvers involving the source term for a class of non homogeneous hyperbolic systems. - 2000-028
:

On the convergence rate of operator splitting for weakly coupled systems of Hamilton-Jacobi equations. - 2000-027
:

Error estimates for approximate solutions for nonlinear scalar conservation laws. - 2000-026
:

Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics. - 2000-025
:

Solution with finite energy to a BGK system relaxing to isentropic gas dynamics. - 2000-024
:

On the spreading of characteristics for nonconvex conservation laws. - 2000-023
:

A strongly degenerate convection-diffusion problem modeling centrifugation of flocculated suspensions. - 2000-022
:

A continuous dependence result for nonlinear degenerate parabolic equations with spatially dependent flux function. - 2000-021
:

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
:

On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations. - 2000-019
:

Asymptotic behavior of solutions of the hydrodynamic model of semiconductors. - 2000-018
:

Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping. - 2000-017
:

Unconditionally stable methods for Hamilton-Jacobi equations. - 2000-016
:

A difference scheme for conservation laws with a discontinuous flux - the nonconvex case. - 2000-015
:

On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients. - 2000-014
:

The Riemann problem for an elastic string with a linear Hooke's law. - 2000-013
:

Numerical experiments with point value multiresolution for 2D compressible flows. - 2000-012
:

Life-span of classical solutions to quasilinear hyperbolic systems with slow decay initial data. - 2000-011
:

An explanation for the sonic point glitch. - 2000-010
:

On some upwind difference schemes for the phenomenological sedimentation-consolidation model. - 2000-009
:

On the convergence of Godunov scheme for nonlinear hyperbolic systems. - 2000-008
:

Central difference solutions of the kinematic model of settling of polydisperse suspensions and three-dimensional particle-scale simulations. - 2000-007
:

On the convergence rate of operator splitting for Hamilton-Jacobi equations with source terms. - 2000-006
:

Approximate Riemann solvers, Godunov schemes, and contact discontinuities. - 2000-005
:

Diffusive BGK approximations for nonlinear multidimensional parabolic equations. - 2000-004
:

Discrete kinetic models for dynamical phase transitions. - 2000-003
:

Long-time diffusive behavior of solutions to a hyperbolic relaxation system. - 2000-002
:

Convergence of a relaxation approximation to a boundary value problem for conservation laws. - 2000-001
:

Operator splitting methods for systems of convection-diffusion equations: nonlinear error mechanisms and correction strategies.

## 1999 Preprints

- 1999-045
:

A note on front tracking and the equivalence between viscosity solutions of Hamilton-Jacobi equations and entropy solutions of scalar conservation laws. - 1999-044
:

Time-periodic solutions for a scalar conservation law. - 1999-043
:

The random projection method for stiff detonation waves. - 1999-042
:

Error estimates on the random projection methods for hyperbolic systems with stiff reaction terms. - 1999-041
:

The random projection method for hyperbolic systems with stiff reaction terms. - 1999-040
:

Hyperbolic systems with supercharacteristic relaxations and roll waves. - 1999-039
:

Operator splitting methods for degenerate convection-diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation. - 1999-038
:

Viscous profiles for traveling waves of scalar balance laws: The canard case. - 1999-037
:

On a Glimm type functional for a special Jin-Xin relaxation model. - 1999-036
:

On the regularity of approximate solutions to conservation laws with piecewise smooth solutions. - 1999-035
:

Pointwise error estimates for relaxation approximations to conservation laws. - 1999-034
:

BV estimates for multicomponent chromatography with relaxation. - 1999-033
:

Global weak solutions to the Navier-Stokes equations for a 1D viscous polytropic ideal gas. - 1999-032
:

Operator splitting methods for degenerate convection-diffusion equations I: convergence and entropy estimates. - 1999-031
:

Gas evolution dynamics and numerical dissipation in shock capturing schemes. - 1999-030
:

On a Lyapunov functional relating shortening curves and viscous conservation laws. - 1999-029
:

First order singular perturbations of quasilinear nonconvex type. - 1999-028
:

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
:

Large time behavior for conservation laws with source in a bounded domain. - 1999-026
:

Initial layers and uniqueness of weak entropy conservation laws. - 1999-025
:

Hamilton-Jacobi equation on a manifold, and applications to mesh generation or refinement. - 1999-024
:

Convergence of a difference scheme for conservation laws with a discontinuous flux. - 1999-023
:

High-resolution hybrid primitive-conservative upwind schemes for the drift flux model. - 1999-022
:

On strongly degenerate convection-diffusion problems modeling sedimentation-consolidation processes. - 1999-021
:

A New general Riemann solver for the shallow water equations, with friction and topography. - 1999-020
:

An analysis of accuracy and convergence of finite volume methods. - 1999-019
:

Granular avalanche flow down a smoothly varying slope: the existence of entropy solutions. - 1999-018
:

Convergence rates for relaxation schemes approximating conservation laws. - 1999-017
:

Numerical solution of the polymer system by front tracking. - 1999-016 Withdrawn by the author.
- 1999-015
:

A fast level set method for reservoir simulation. - 1999-014
:

Periodic solutions of conservation laws constructed through Glimm scheme. - 1999-013
:

A note on the Riemann problem for general nxn conservation laws. - 1999-012
:

Well-posedness for general 2x2 systems of conservation laws. - 1999-011
:

New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations - 1999-010
:

Relaxation of the isothermal Euler-Poisson system to the drift-diffusion equations - 1999-009
:

A numerical study of a pathological example of p-system. - 1999-008
:

Resurrection of "second order" models of car traffic ? - 1999-007
:

Stability of a resonant system of conservation laws modeling polymer flow with gravitation - 1999-006
:

Numerical methods for the simulation of the settling of flocculated suspensions - 1999-005
:

Numerical simulation of the settling of polydisperse suspensions of spheres - 1999-004
:

Vanishing viscosity solutions of hyperbolic systems on manifolds - 1999-003
:

Operator splitting methods for generalized Korteweg-de Vries equations - 1999-002
:

Entropy analysis of kinetic flux vector splitting schemes for the compressible Euler equations. - 1999-001
:

Numerical solution of reservoir flow models based on large time step operator splitting algorithms.

## 1998 Preprints

- 1998-042
:

Large-time behavior of solutions to the equations of a one-dimensional viscous polytropic ideal gas in unbounded domains. - 1998-041
:

A two-dimensional HLLE Riemann solver and associated Godunov-type difference scheme for gas dynamics. - 1998-040
:

Granular avalanche flow down a smoothly varying slope: the existence of entropy solutions. - 1998-039
:

Stability of L$^\infty$ solutions of Temple class systems. - 1998-038
:

Uniformly accurate diffusive relaxation schemes for multiscale transport equations. - 1998-037
:

Zero reaction limit for hyperbolic conservation laws with source terms. - 1998-036
:

Global BV solutions and relaxation limit for a system of conservation laws. - 1998-035
:

Composite centered schemes for multidimensional conservation laws. - 1998-034
:

Construction of BGK models with a family of kinetic entropies for a given system of conservation laws. - 1998-033
:

A uniqueness condition for hyperbolic systems of conservation laws. - 1998-032
:

On the Cauchy problem for nonlinear hyperbolic systems. - 1998-031
:

Hyperbolic systems of conservation laws. - 1998-030
:

L^1 stability estimates for n x n conservation laws. - 1998-029
:

Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws. - 1998-028
:

Stability of viscous shock waves associated with non-convex modes. - 1998-027
:

Diffusion limit of a hyperbolic system with relaxation. - 1998-026
:

Relaxation schemes for curvature-dependent front propagation. - 1998-025
:

Gas evolution dynamics in Godunov-type schemes. - 1998-024
:

Explicit finite difference schemes for the advection equation. - 1998-023
:

A note on the spreading of characteristics for nonconvex conservation laws. - 1998-022
:

Approximate solutions of nonlinear conservation laws and related equations. - 1998-021
:

The zero relaxation limit for $2\times 2$ hyperbolic systems. - 1998-020
:

Moving-mesh methods for one-dimensional hyperbolic problems using CLAWPACK. - 1998-019
:

Unconditionally stable splitting methods for the shallow water equations. - 1998-018
:

An unconditionally stable method for the Euler equations. - 1998-017
:

Discrete approximations of BV solutions to doubly nonlinear degenerate parabolic equations. - 1998-016
:

On the homogenization of oscillatory solutions to nonlinear convection-diffusion equations - 1998-015
:

$L^1$-stability and error estimates for approximate Hamilton-Jacobi solutions - 1998-014
:

Degenerate convection-diffusion equations and implicit monotone difference schemes. - 1998-013
:

A front tracking method for conservation laws with boundary conditions. - 1998-012
:

Rate of convergence for the zero relaxation limit. - 1998-011
:

Monotone difference approximations of BV solutions to degenerate convection-diffusion equations. - 1998-010
:

Heteroclinic orbits between rotating waves in hyperbolic balance laws. - 1998-009
:

Numerical schemes for kinetic equations in diffusive regimes. - 1998-008
:

Blowup for systems of conservation laws. - 1998-007
:

Pointwise error estimates for scalar conservation laws with piecewise smooth solutions. - 1998-006
:

Blowup asymptotics for scalar conservation laws with a source. - 1998-005
:

High-resolution finite volume methods for acoustics in a rapidly-varying heterogeneous medium. - 1998-004
:

Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propogation algorithm. - 1998-003
:

A study of the modelling error in two operator splitting algorithms for porous media flow. - 1998-002
:

The corrected operator splitting approach applied to an advection-diffusion problem. - 1998-001
:

Singular perturbations of first-order hyperbolic systems with stiff source terms

## 1997 Preprints

- 1997-037
:

Stability of conservation laws with discontinuous coefficients - 1997-036
:

Continuous dependence in the large for some equations of gas dynamics - 1997-035
:

Oleinik type estimates and uniqueness for n x n conservation laws - 1997-034
:

2D shallow water equations by composite schemes - 1997-033
:

Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems - 1997-032
:

Stiff well-posedness and asymptotic expansions for hyperbolic systems with relaxation - 1997-031
:

A dimensional splitting method for nonlinear equations with variable coefficients - 1997-030
:

Front tracking for one-dimensional nonlinear advection equations with variable coefficients - 1997-029
:

Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations - 1997-028
:

Viscous splitting approximation of mixed hyperbolic-parabolic convection-diffusion equations - 1997-027
:

Nonclassical shocks and the Cauchy problem for nonconvex conservation laws - 1997-026
:

Numerical passage from systems of conservation laws to Hamilton-Jacobi equations, and a relaxation scheme - 1997-025
:

Scalar non-linear conservation laws with integrable boundary data - 1997-024
:

On the attainable set for scalar non-linear conservation laws with boundary control - 1997-023
:

Hyperbolic conservation laws with a moving source - 1997-022
:

A simple approach to Glimm's interaction estimates - 1997-021
:

Diffusive relaxation schemes for discrete-velocity kinetic equations - 1997-020
:

Relaxation approximations to front propagation - 1997-019
:

Triple shock entropy theorem and its consequences - 1997-018
:

Composite schemes for conservation laws - 1997-017
:

Convergence of explicit finite volume schemes for Friedrichs Systems - 1997-016
:

An unconditionally stable splitting scheme for a class nonlinear parabolic equations - 1997-015
:

A note on viscous splitting of degenerate convection-diffusion equations - 1997-014
:

Hyperbolic to parabolic relaxation theory for quasilinear first order systems - 1997-013
:

Non-oscillatory central schemes for multidimensional hyperbolic conservation laws - 1997-012
:

Third order nonoscillatory central scheme for hyperbolic conservation laws - 1997-011
:

A front tracking approach to a two-phase fluid flow model with capillary forces - 1997-010
:

Corrected operator splitting for nonlinear parabolic equations - 1997-009
:

Local existence and stability for a hyperbolic–elliptic system modeling two–phase reservoir flow - 1997-008
:

A difference scheme for a stiff system of conservation laws - 1997-007
:

On the zero relaxation limit for a system modeling the motions of a viscoelastic solid - 1997-006
:

Uniqueness for discontinuous O.D.E. and conservation laws - 1997-005
:

Qualitative behavior of conservation laws with reaction term and nonconvex flux - 1997-004
:

The zero relaxation limit for the hydrodynamic Whitham traffic flow model - 1997-003
:

A wave propagation method for three-dimensional hyperbolic conservation laws - 1997-002
:

Well-posedness of the Cauchy problem for nxn systems of conservation laws - 1997-001
:

Projection dynamics in Godunov-type schemes i: to the physical understanding of post-shock oscillations

## 1996 Preprints

- 1996-044
:

Well-posedness for a class of $2\times 2$ conservation laws with $L^\infty$ data - 1996-043
:

Decay of positive waves in nonlinear systems of conservation laws

- 1996-042
:

The semigroup approach to systems of conservation laws - 1996-041
:

The perturbed riemann problem for a balance law - 1996-040
:

Lower semicontinuity of weighted path length in BV - 1996-039
:

Large time behavior of the solutions to a hydrodynamic model for semiconductors - 1996-038
:

Identification of mobilities for the Buckley-Leverett equation by front tracking - 1996-037
:

On the front tracking algorithm - 1996-036
:

Convergence analysis for operator splitting methods to conservation laws with stiff source terms - 1996-035
:

Unsplitting BGK-type schemes for the shallow water equations - 1996-034
:

The energy transport and the drift diffusion equations as relaxation limits of the hydrodynamic model for semiconductors - 1996-033
:

Riemann problems with a kink - 1996-032
:

Error bounds for a deterministic version of the Glimm scheme - 1996-031
:

The semigroup generated by a Temple class system with large data - 1996-030
:

Higher order discretisation of initial-boundary value problems for mixed systems - 1996-029
:

Stiff well-posedness for hyperbolic systems with large relaxation terms - 1996-028
:

Compact difference methods applied to initial-boundary value problems for mixed systems - 1996-027
:

Finite difference schemes for scalar conservation laws with source terms - 1996-026
:

Convergence of implicit finite difference methods applied to nonlinear mixed systems - 1996-025
:

Viscosity methods for piecewise smooth solutions to scalar conservation laws - 1996-024
:

Discontinuous solutions of the Navier-Stokes equations for multidimensional heat-conducting flow - 1996-023
:

A finite element method for fully nonlinear water waves - 1996-022
:

A system of conservation laws with a relaxation term - 1996-021
:

An error bound for a finite difference scheme applied to a stiff system of conservation laws - 1996-020
:

On the rate of convergence to equilibrium for a system of conservation laws including a relaxation term - 1996-019
:

A system of conservation laws including a stiff relaxation term; the 2D case - 1996-018
:

Error bounds of finite difference schemes for two-dimensional scalar conservation laws with source term - 1996-017
:

Shift-differentiability of the flow generated by a conservation law - 1996-016
:

Travelling wave solutions for a balance law - 1996-015
:

Multiscale concept for conservation laws - 1996-014
:

Uniqueness of weak solutions to systems of conservation laws - 1996-013
:

Weakly coupled systems of quasilinear hyperbolic equations - 1996-012
:

A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws - 1996-011
:

L^1 nonlinear stability of travelling waves for a hyperbolic system with relaxation - 1996-010
:

How parabolic free boundaries approximate hyperbolic fronts - 1996-009
:

On the Chapman-Jouguet Limit for a combustion model - 1996-008
:

A discrete approximation for hyperbolic systems with quadratic interaction term - 1996-007
:

Convergence of relaxation schemes for conservation laws - 1996-006
:

Convergence to equilibrium for the relaxation approximations of conservation laws - 1996-005
:

Conservation laws with vanishing nonlinear diffusion and dispersion - 1996-004
:

Global weak entropy solutions to quasilinear wave equations of Klein–Gordon and Sine–Gordon Type - 1996-003
:

Conservation laws with a random source - 1996-002
:

An operator splitting method for convection-diffusion equations - 1996-001
:

Dimensional splitting with front tracking and adaptive local grid refinement.