Inverse scattering for the one-dimensional Stark effect and application to the cylindrical KdV equation
Inverse scattering problem for moving obstacles.
Inverse scattering problem for the Maxwell equations outside moving body
Inverse scattering problems in several dimensions
Inverse scattering theory for Dirac operators
Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data
We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to...
Jost solution and the spectrum of the discrete Dirac systems.
Klein Paradox and Superradiance for the charged Klein-Gordon Field
La structure de la matrice pour le problème à trois corps
Limiting absorption principle for the Dirac operator
Local decay estimates for Schrödinger operators with long range potentials
Local Decay in time of solutions to Schrödinger's equation with a dilation-analytic interaction.
Local energy decay for several evolution equations on asymptotically euclidean manifolds
Let be a long range metric perturbation of the Euclidean Laplacian on , . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger equations associated to . The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group where has a suitable development at zero (resp. infinity).
Long range scattering and modified wave operators for Hartree equations
We study the theory of scattering for the Hartree equation with long range potentials. We prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.
Long range scattering with Stark effect and almost periodic potentials.
Long-range many-body scattering.
Long-range scattering of two- and three-body quantum systems
Low-Frequency electromagnetic scattering theory for a dielectric
Majoration du nombre de résonances près de l'axe réel (d'après un travail avec M. Zworski)
Mathematical modeling of time-harmonic aeroacoustics with a generalized impedance boundary condition
We study the time-harmonic acoustic scattering in a duct in presence of a flow and of a discontinuous impedance boundary condition. Unlike a continuous impedance, a discontinuous one leads to still open modeling questions, as in particular the singularity of the solution at the abrupt transition and the choice of the right unknown to formulate the scattering problem. To address these questions we propose a mathematical approach based on variational formulations set in weighted Sobolev spaces. Considering...