Magnetic barriers of compact support and eigenvalues in spectral gaps.
Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics
I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.
Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint
This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied magnetic field for vortex nucleation is estimated in the London singular limit, and as a by-product, results concerning vortex-pinning and boundary conditions on the interface are obtained.
Majoration de multiplicité pour l'opérateur de Schrödinger
Majoration du nombre de résonances près de l'axe réel (d'après un travail avec M. Zworski)
Majoration en norme hölderienne de la résolvante du laplacien dans un ouvert avec coins
Majorations a priori et problèmes frontière elliptiques du second ordre
Manifolds of Dimension 3 with Prescribed Positive Curvature and with Nontrivial Homology.
Marchuk identity-type second order difference schemes of 2-d and 3-d elliptic problems with intersected interfaces
Martin boundary for Schrödinger operators with singularity.
Martin compactification and asymptotics of Green functions for Schrödinger operators with anisotropic potentials.
Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates
We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between...
Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy–Forchheimer flow in the fracture
We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy−Forchheimerlaw while that in the surrounding matrix is governed by Darcy’s law. We give an appropriate mixed, variational formulation and show existence and uniqueness of the solution. To show existence we give an analogous formulation for the model in which the Darcy−Forchheimerlaw is the governing equation throughout the domain. We show existence and uniqueness of the solution...
Mathematical approach and numerical analysis to the fundamental solutions method of Dirichlet problem.
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...
Mathematical modelling of an electrolysis process
Mathematical study of rotational incompressible non-viscous flows through multiply connected domains
The paper is devoted to the study of the boundary value problem for an elliptic quasilinear second-order partial differential equation in a multiply connected, bounded plane domain under the assumption that the Dirichlet boundary value conditions on the separate components of the boundary are given up to additive constants. These constants together with the solution of the equation considered are to be determined so as to fulfil the so called trainling conditions. The results have immediate applications...
Matrices de diffusion pour l'opérateur de Schrödinger avec champ magnétique et phénomène de Aharonov-Bohm
Maximal and Minimal Solutions of Elliptic Differential Equations with Discontinuous Non-Linearities.
Maximal inequalities and Riesz transform estimates on spaces for Schrödinger operators with nonnegative potentials
We show various estimates for Schrödinger operators on and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of and their gradients.