DIFTA
Differential Equations in
Theory and
Applications
Spring term 2007
The topic is differential equations (both partial and ordinary
differential equations).
Unless otherwise noted, talks are
Wednesdays, 14:15–15:00 in room 734, S-2.
| Date | Speaker | Title |
|---|
|
2007-01-24
14:15–15:00 |
Xavier Raynaud |
Unique solutions of discontinuous O.D.E.
(abstract). |
2007-02-07
14:15–15:00 |
David Cohen |
Long-time analysis of nonlinearly perturbed
wave equations via modulated Fourier expansions
(Abstract:
A modulated Fourier expansion in time is used to study
the long-time behaviour of nonlinear wave equations
with small initial data.
The result shows that the actions remains nearly constant over
long times.
It also implies the near-preservation, over such long times,
of the Sobolev-type norm that specifies the
smallness condition on the initial data.) |
2007-02-14
14:15–15:00 |
Fabio Camilli (L'Aquila, Italia) |
Random perturbed dynamical systems and Aubry–Mather theory
(Abstract: I will describe a new PDE proof
of the Freidlin–Wentzell theorem about the exit points
from a domain of a random process,
obtained by perturbing a dynamical system through the addition of a small noise.
The relevant part of the analysis concerns an Hamilton–Jacobi equation,
coupled with a Neumann boundary condition,
which does not possess any strict subsolution.
The method exploits the viscosity solution theory and the
so-called metric approach to Hamilton–Jacobi equations.) |
2007-02-21
14:15–15:00 |
Christine Georgelin |
Continuous dependence results for non-linear
Neumann type boundary value Problems
(abstract). |
2007-02-28
14:15–16:00 |
Fabio Priuli |
Nash Equilibrium Solutions for Infinite Horizon Differential Games
(Abstract:
In this seminar, I will give an introduction to the study of
Nash equilibrium solution for a particular class of
non-cooperative non-zero sum differential games.
This problem is related, through the value function of the game,
to the study of the existence of solutions for a system of
Hamilton–Jacobi equations.
Since the game has non-zero sum,
the system cannot be reduced to a single HJ equation
and therefore standard tools of viscosity solutions theory
cannot be applied.
Very few results are known on the matter,
and I will present a couple of cases in which
either positive or negative results can be still recovered,
provided the cost functions the players want to minimize
have a good behaviour (but are not necessarily smooth)) |
2007-03-14
14:15–15:00 |
Fabio Priuli |
Nearly Optimal Feedback Controls
(abstract) |
2007-03-21
14:15–15:00 |
Larisa Beilina |
A posteriori error estimation in computational inverse scattering:
application to photonic crystal (abstract). |
2007-04-18
14:15–15:00 |
V.G. Danilov |
Some problems of nonlinear solitary waves
interaction in nonintegrable systems
(abstract). |
| 2007-04-25 |
Achenef Tesfahun Temesgen |
Low regularity well-posedness for the one dimensional
Dirac–Klein–Gordon system
(Abstract:
In this talk we will present a proof of low regularity well-posedness
of the Dirac–Klein–Gordon (DKG) system in one space dimension,
which is an extension of recent results of S. Machihara and H. Pecher.
Our proof, like that of Pecher, relies on the null structure of DKG,
recently completed by D'Ancona, Foschi and Selberg,
but we show that in 1d the argument can be simplified by modifying
the choice of projections for the Dirac operator.) |
2007-05-09
14:15–15:00 |
Mikko Parviainen |
Global higher integrability for parabolic quasiminimizers |
2007-05-23
14:15–15:00 |
Henrik Kalisch |
On the Rate of Convergence of a Spectral Approximation
of the KdV Equation
(Abstract:
Spectral methods are a popular choice for the numerical
approximation of nonlinear evolution equations.
One of the advantages of spectral methods is the
rapid convergence, making it possible to achieve
high accuracy in computations with relatively few grid points.
Indeed, it can often be proved that spectral projections
feature convergence rates that are higher than any algebraic power.
In this lecture, we will focus on the KdV equation.
It will be shown that when the initial data is analytic,
then the convergence rate is actually exponential.
This result agrees well with numerical experiments
which also exhibit exponential convergence.) |
2007-06-06
14:15–15:00 |
David Kalaj, University of Montenegro |
On the univalent solution of PDE
Δu=f between spherical annuli
(Abstract: It is proved that if
u=(u1,u2,u3)
is the solution of PDE
Δu=(f1,f2,f3)
that maps two annuli on the space R3,
then the annulus in co-domain cannot be with arbitrary small modulus,
providing that the annulus of domain is fixed.
Also it is improved previously obtained inequality
for harmonic functions in R3.
Finally it is given the new conjecture for harmonic mappings in
the space similar to the conjecture of J. C. C. Nitsche
for harmonic mapping in the plane related to the modulus of annuli.)
|
2007-06-14
(Thursday!)
room 922
11:15–12:00 |
Cyril Imbert |
On the Dirichlet problem for second-order elliptic
integro-differential equations |
- Earlier seminars
-
2006 spring, fall;
2005 spring, fall;
2004 spring, fall;
2003 spring, fall;
2002 spring,
fall;
2001 spring,
fall;
2000 spring,
fall;
1999 fall.
Se også Ukeplanen
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