Gilles Carbou

THIN LAYERS IN MICROMAGNETISM

In this paper we study the solutions of micromagnetism equation in thin domain both in the stationary and in the time-dependent case. We prove that the magnetic field induced by the magnetisation b...

Unicité et minimalité des solutions d'une équation de Ginzburg-Landau

Resume On etudie les solutions de l’equation −∆u + u(u2 − 1) = 0, ou u est element de H l o c 1 ( ℝ n ) . On montre que la solution f ( x 1 , … , x n ) = t h ( x 1 2 ) minimise l’energie parmi les fonctions tendant vers −1 lorsque x1 tend vers −∞ et vers +1 lorsque x1 tend vers +∞. De plus, on prouve que toute solution de l’equation qui tend vers 1 lorsque |x| tend vers +∞ est constante egale a 1 sur ℝn.

Relaxed model for the hysteresis in micromagnetism

In this paper we study a model of ferromagnetic material with hysteresis effects. The magnetic moment behaviour is described by the non-linear Landau-Lifschitz equation with an additional term modelling the hysteresis. This term takes the form of a maximal monotone operator acting on the time derivative of the magnetic moment. In our model, it is approximated via a relaxing heat equation. For this relaxed model we prove local existence of regular solutions.

Stability for Walls in Ferromagnetic Nanowire

We study the stability of travelling wall profiles for a one dimensional model of ferromagnetic nanowire submitted to an exterior magnetic field. We prove that these profiles are asymptotically stable modulo a translation-rotation for small applied magnetic fields.

Relaxation approximation of the Kerr Model for the three dimensional initial-boundary value problem

The electromagnetic wave propagation in a nonlinear medium is described by the Kerr model in the case of an instantaneous response of the material, or by the Kerr–Debye model if the material exhibits a finite response time. Both models are quasilinear hyperbolic and are endowed with a dissipative entropy. The initial-boundary value problem with a maximal-dissipative impedance boundary condition is considered here. When the response time is fixed, in both the one-dimensional and two-dimensional transverse electric cases, the global existence of smooth solutions for the Kerr–Debye system is established. When the response time tends to zero, the convergence of the Kerr–Debye model to the Kerr model is established in the general case, i.e. the Kerr model is the zero relaxation limit of the Kerr–Debye model.

A remark on the weak ω-limit set for micromagnetism equation

Abstract In this paper, we give a complete characterization of the weak ω-limit set for a system of partial differential equations arising in micromagnetism theory, in which Maxwell equations are coupled with the Landau-Lifschitz equation for the magnetic moment.

Modèle quasi-stationnaire en micromagnétisme

Resume On montre que les solutions du modele complet du ferromagnetisme tendent vers les solutions du modele quasi-stationnaire lorsque la permittivite dielectrique e 0 tend vers zero.