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Decay of solutions of the wave equation in the exterior of several convex bodies
We study the decay of solutions to the wave equation in the exterior of several strictly convex bodies. A sufficient condition for exponential decay of the local energy is expressed in terms of the period and the Poincare map of periodic rays in the exterior domain.
Derivation of high-order spectral methods for time-dependent PDE using modified moments.
Determining the parameters of a stratified piecewise constant medium for the unknown shape of an impulse source.
Deuxième microlocalisation et problèmes aux limites
Diffraction des singularités analytiques dans les problèmes aux limites de la physique mathématique par les méthodes de Kawai-Kashiwara et Sjöstrand
Dirichlet and Neumann problems for string equation, Poncelet problem and Pell-Abel equation.
Discontinous Solutions of a Nonlinear Hyperbolic Equation with Unilateral Constraints.
Discontinuous wave equations and a topological degree for some classes of multi-valued mappings
The Leray-Schauder degree is extended to certain multi-valued mappings on separable Hilbert spaces with applications to the existence of weak periodic solutions of discontinuous semilinear wave equations with fixed ends.
Dispersive and Strichartz estimates for the wave equation in domains with boundary
In this note we consider a strictly convex domain of dimension with smooth boundary and we describe the dispersive and Strichartz estimates for the wave equation with the Dirichlet boundary condition. We obtain counterexamples to the optimal Strichartz estimates of the flat case; we also discuss the some results concerning the dispersive estimates.
Dispersive estimates for a linear wave equation with electromagnetic potential.
Distribution near the real axis of scattering poles generated by a non-hyperbolic periodic ray
Distributions and heat equation in
Divergence boundary conditions for vector Helmholtz equations with divergence constraints
The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.