Shear layer solutions of incompressible MHD and dynamo effect
Singularities of eddy current problems
We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of Bossavit [11]. We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace operator,...
Singularities of eddy current problems
We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of Bossavit [11]. We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace...
Singularities of Maxwell interface problems
Singularities of Maxwell interface problems
We investigate time harmonic Maxwell equations in heterogeneous media, where the permeability μ and the permittivity ε are piecewise constant. The associated boundary value problem can be interpreted as a transmission problem. In a very natural way the interfaces can have edges and corners. We give a detailed description of the edge and corner singularities of the electromagnetic fields.
Singularities of Maxwell’s system in non-hilbertian Sobolev spaces
We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space and an explicit singular one.
Solutions explosives exceptionnelles
Solutions globales du système de Maxwell dans un milieu ferromagnétique
Solutions stationnaires des équations de Vlasov-Poisson à symétries cylindriques
Solutions to a nonlinear drift-diffusion model for semiconductors.
Some generalized Poincaré inequalities and applications to problems arising in electromagnetism.
Some initial boundary problems in electrodynamics for canonical domains in quaternions
The initial boundary-transmission problems for electromagnetic fields in homogeneous and anisotropic media for canonical semi-infinite domains, like halfspaces, wedges and the exterior of half- and quarter-plane obstacles are formulated with the use of complex quaternions. The time-harmonic case was studied by A. Passow in his Darmstadt thesis 1998 in which he treated also the case of an homogeneous and isotropic layer in free space and above an ideally conducting plane. For thin layers and free...
Some new results in multiphase geometrical optics
Some new results in multiphase geometrical optics
In order to accommodate solutions with multiple phases, corresponding to crossing rays, we formulate geometrical optics for the scalar wave equation as a kinetic transport equation set in phase space. If the maximum number of phases is finite and known a priori we can recover the exact multiphase solution from an associated system of moment equations, closed by an assumption on the form of the density function in the kinetic equation. We consider two different closure assumptions based on delta...
Some rigorous results on the Pauli-Fierz model of classical electrodynamics
Spectral properties of high contrast band-gap materials and operators on graphs.
Stabilité des solitons de l’équation de Landau-Lifshitz à anisotropie planaire
Cet exposé présente plusieurs résultats récents quant à la stabilité des solitons sombres de l’équation de Landau-Lifshitz à anisotropie planaire, en particulier, quant à la stabilité orbitale des trains (bien préparés) de solitons gris [16] et à la stabilité asymptotique de ces mêmes solitons [2].
Stability and controllability of the electromagneto-elastic system.
Stabilization of heterogeneous Maxwell's equations by linear or nonlinear boundary feedbacks.
Stabilization of walls for nano-wires of finite length
In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.