The Wigner–Poisson–Fokker–Planck system : global-in-time solution and dispersive effects
The WKB method and geometric instability for nonlinear Schrödinger equations on surfaces
In this paper we are interested in constructing WKB approximations for the nonlinear cubic Schrödinger equation on a Riemannian surface which has a stable geodesic. These approximate solutions will lead to some instability properties of the equation.
The Wolff gradient bound for degenerate parabolic equations
The spatial gradient of solutions to non-homogeneous and degenerate parabolic equations of -Laplacean type can be pointwise estimated by natural Wolff potentials of the right hand side measure.
The Yang-Mills gradient flow in four dimensions
The zero set of a solution of a parabolic equation.
The -Neumann operator on strongly pseudoconvex domain with piecewise smooth boundary
Théorème de Cauchy-Kovalevsky et théorème d'unicité d'Holmgren pour des fonctions analytiques d'une infinité de variables
Théorème d'indice et régularité pour une classe d'opérateurs elliptiques et dégénérés
Théorème d'indice et régularité pour une classe d'opérateurs elliptiques et dégénérés
Théorème d'indice pour une classe d'opérateurs elliptiques fortement dégénérés sur la frontière
Théorème du point fixe et théorème de Cauchy-Kowalewsky-Lednev pour les systèmes semi-linéaires
Théorèmes de régularité locale pour des systèmes elliptiques dégénérés et des problèmes non différentiables
Théorèmes d'indice pour des opérateurs différentiels à coefficients polynomiaux
Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part
Theorems on -dimensional Laplace transforms and their applications.
Theoretical analysis of a model of the thermal boundary layer with drag.
Theoretical and numerical aspects of stochastic nonlinear Schrödinger equations
We describe several results obtained recently on stochastic nonlinear Schrödinger equations. We show that under suitable smoothness assumptions on the noise, the nonlinear Schrödinger perturbed by an additive or multiplicative noise is well posed under similar assumptions on the nonlinear term as in the deterministic theory. Then, we restrict our attention to the case of a focusing nonlinearity with critical or supercritical exponent. If the noise is additive, smooth in space and non degenerate,...
Theoretical and numerical study of a free boundary problem by boundary integral methods
In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.
Theoretical and numerical study of a free boundary problem by boundary integral methods
In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.
Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping
In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for the...