Paramétrix du problème mixte pour l'équation des ondes à l'intérieur d'un domaine convexe pour les bicaractéristiques
Periodic Solutions of a Nonlinear Wave Equation Without Assumption of Monotonicity.
Perturbations singulières d'équations hyperboliques du second ordre non linéaires
Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation. II
Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation
We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition. We are interested to the asymptotic behavior for large times for the solution, and in particular to the dependence on the norms of the initial data in the estimate for the pointwise decay rate. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.
Problemes aux limites non classiques pour equations d'evolution.
Propagation de singularités pour des problèmes aux limites d'ordre 2
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 along gliding rays
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, reflection and refraction of singularities for a hyperbolic transmission problem in two adjacent angular regions
Pseudomonotonicity and nonlinear hyperbolic equations
In this paper we consider a nonlinear hyperbolic boundary value problem. We show that this problem admits weak solutions by using a lifting result for pseudomonotone operators and a surjectivity result concerning coercive and monotone operators.