Estimates of the heat content on a class of domains.
Estimates on the number of scattering poles near the real axis for strictly convex obstacles
For the Dirichlet Laplacian in the exterior of a strictly convex obstacle, we show that the number of scattering poles of modulus in a small angle near the real axis, can be estimated by Const for sufficiently large depending on . Here is the dimension.
Estimation des résidus de la matrice de diffusion associés à des résonances de forme I
Estimations de diffusion pour un opérateur de Klein-Gordon matriciel dépendant du temps
Estimations exponentielles en théorie de la diffusion pour des opérateurs de Schrödinger matriciels
Estimations sur l'effet tunnel microlocal
Evolution by the vortex filament equation of curves with a corner
In this proceedings article we shall survey a series of results on the stability of self-similar solutions of the vortex filament equation. This equation is a geometric flow for curves in and it is used as a model for the evolution of a vortex filament in fluid mechanics. The main theorem give, under suitable assumptions, the existence and description of solutions generated by curves with a corner, for positive and negative times. Its companion theorem describes the evolution of perturbations...
Existence des opérateurs d'ondes pour les systèmes hyperboliques avec un potentiel périodique en temps
Focusing of a pulse with arbitrary phase shift for a nonlinear wave equation
We consider a system of two linear conservative wave equations, with a nonlinear coupling, in space dimension three. Spherical pulse like initial data cause focusing at the origin in the limit of short wavelength. Because the equations are conservative, the caustic crossing is not trivial, and we analyze it for particular initial data. It turns out that the phase shift between the incoming wave (before the focus) and the outgoing wave (past the focus) behaves like , where stands for the wavelength....
Formules de trace, résonances et quasi-modes
Fractal Weyl laws for quantum resonances
Generalized Backscattering and the Lax-Phillips Transform
2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle w = Sq in terms of the incoming angle with S orthogonal and Id-S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact support. As a corollary we show that the...
Global smooth solutions to a class of semilinear wave equations with strong nonlinearities.
Global solutions of quasilinear systems of Klein–Gordon equations in 3D
We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations for electrons.
Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data.
High energy asymptotics for N-body scattering matrices with arbitrary channels
Homogeneous estimates for oscillatory integrals.
Intertwining methods in the problem of inverse scattering
Inverse problems and microlocal analysis
Inverse Scattering at fixed energy for stratified media