Inverse Scattering at fixed energy for stratified media
Inverses d'opérateurs faiblement hyperboliques à caractéristiques de multiplicité variable dans la classe des opérateurs de Volterra
Investigations of retarded PDEs of second order in time using the method of inertial manifolds with delay
Inertial manifold with delay (IMD) for dissipative systems of second order in time is constructed. This result is applied to the study of different asymptotic properties of solutions. Using IMD, we construct approximate inertial manifolds containing all the stationary solutions and give a new characterization of the K-invariant manifold.
Involutivity and Symple Waves in R^2
A strictly hyperbolic quasi-linear 2×2 system in two independent variables with C2 coefficients is considered. The existence of a simple wave solution in the sense that the solution is a 2-dimensional vector-valued function of the so called Riemann invariant is discussed. It is shown, through a purely geometrical approach, that there always exists simple wave solution for the general system when the coefficients are arbitrary C^2 functions depending on both, dependent and independent variables.
Is GPU the future of Scientific Computing ?
These past few years, new types of computational architectures based on graphics processors have emerged. These technologies provide important computational resources at low cost and low energy consumption. Lots of developments have been done around GPU and many tools and libraries are now available to implement efficiently softwares on those architectures.This article contains the two contributions of the mini-symposium about GPU organized by Loïc Gouarin (Laboratoire de Mathématiques d’Orsay),...
Jumping nonlinearities and mathematical models of suspension bridge
Justification de l'optique géométrique non linéaire pour un système de lois de conservation
Justification of the steepest descent method for the integral statement of an inverse problem for a hyperbolic equation.
KAM theory for the hamiltonian derivative wave equation
We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations.
Kelvin principle for a class of singular equations.
Kinetic approach to systems of conservation laws
Kinetic formulation for heterogeneous scalar conservation laws
Kink-antikink interaction for semilinear wave equations with a small parameter.
Kirchhoff-Carrier elastic strings in noncylindrical domains.
Klein-Gordon type decay rates for wave equations with time-dependent coefficients
This work is concerned with the proof of decay estimates for solutions of the Cauchy problem for the Klein-Gordon type equation . The coefficient consists of an increasing smooth function and an oscillating smooth and bounded function b which are uniformly separated from zero. Moreover, is a positive constant. We study under which assumptions for λ and b one can expect as an essential part of the decay rate the classical Klein-Gordon decay rate n/2(1/p-1/q).
Kolmogorov's epsilon-entropy of the attractor of the strongly damped wave equation in locally uniform spaces
We establish an upper bound on the Kolmogorov’s entropy of the locally compact attractor for strongly damped wave equation posed in locally uniform spaces in subcritical case using the method of trajectories.
singular limit for relaxation and viscosity approximations of extended traffic flow models.
stability of conservation laws for a traffic flow model.
-type contraction for systems of conservation laws
The semi-group associated with the Cauchy problem for a scalar conservation law is known to be a contraction in . However it is not a contraction in for any . Leger showed in [20] that for a convex flux, it is however a contraction in up to a suitable shift. We investigate in this paper whether such a contraction may happen for systems. The method is based on the relative entropy method. Our general analysis leads us to the new geometrical notion of Genuinely non-Temple systems. We treat in...
well-posed Cauchy problems and symmetrizability of first order systems
The Cauchy problem for first order system is known to be well-posed in when it admits a microlocal symmetrizer which is smooth in and Lipschitz continuous in . This paper contains three main results. First we show that a Lipschitz smoothness globally in is sufficient. Second, we show that the existence of symmetrizers with a given smoothness is equivalent to the existence of full symmetrizers having the same smoothness. This notion was first introduced in [FL67]. This is the key point...