Periodic solutions of a weakly nonlinear wave equation in one dimension
Periodic solutions of asymptotically linear systems without symmetry
Periodic solutions to a one-dimensional strongly nonlinear wave equation with strong dissipation
Periodic solutions to the inhomogeneous sine-Gordon equation
Periodic solutions to weakly nonlinear autonomous wave equations
Perte de régularité pour les équations d’ondes sur-critiques
On prouve que le problème de Cauchy local pour l’équation d’onde sur-critique dans , , impair, avec et , est mal posé dans pour tout , où est l’exposant critique.
Pointwise controllability as limit of internal controllability for the wave equation in one space dimension.
Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation. II
Pointwise Fourier Inversion: a Wave Equation Approach.
Pointwise Fourier Inversion on Tori and Other Compact Manifolds.
Probabilistic well-posedness for the cubic wave equation
The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We restrict the study to one of the simplest examples of such equations: the periodic cubic semi-linear wave equation. Our contributions in this work are twofold: first we break the algebraic rigidity involved in our previous works and allow much more general randomizations (general infinite product measures v.s. Gibbs...
Problème spectrale concernant l'opérateur de Laplace et les domaines des polyèdres générés par le systéme de racines de type C.
Propagation des ondes dans les dièdres
Propagation des ondes dans les dièdres
Propagation des ondes dans les variétés à coins
Propagation et réflexion de la propriété de transmission des distributions de Fourier
Propagation of singularities for the wave equation on manifolds with corners
In this talk we describe the propagation of and Sobolev singularities for the wave equation on manifolds with corners equipped with a Riemannian metric . That is, for , , and solving with homogeneous Dirichlet or Neumann boundary conditions, we show that is a union of maximally extended generalized broken bicharacteristics. This result is a counterpart of Lebeau’s results for the propagation of analytic singularities on real analytic manifolds with appropriately stratified boundary,...
Propagation through trapped sets and semiclassical resolvent estimates
Motivated by the study of resolvent estimates in the presence of trapping, we prove a semiclassical propagation theorem in a neighborhood of a compact invariant subset of the bicharacteristic flow which is isolated in a suitable sense. Examples include a global trapped set and a single isolated periodic trajectory. This is applied to obtain microlocal resolvent estimates with no loss compared to the nontrapping setting.
Propriétés asymptotiques des vibrations des tores
Quasilinear waves and trapping: Kerr-de Sitter space
In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally...