Olivier Vacus

Well-posed absorbing layer for hyperbolic problems

Summary. The perfectly matched layer (PML) is an efficient tool to simulate propagation phenomena in free space on unbounded domain. In this paper we consider a new type of absorbing layer for Maxwells equations and the linearized Euler equations which is also valid for several classes of first order hyperbolic systems. The definition of this layer appears as a slight modification of the PML technique. We show that the associated Cauchy problem is well-posed in suitable spaces. This theory is finally illustrated by some numerical results. It must be underlined that the discretization of this layer leads to a new discretization of the classical PML formulation.

On transitions to stationary states in a Maxwell-Landau-Lifschitz-Gilbert system

In this paper we consider Maxwells equations together with a dissipative nonlinear magnetic law, the Landau--Lifschitz--Gilbert equation, and we study long-time asymptotics of solutions in the 1D case in an infinite domain of propagation. We prove long-time convergence to zero of the electromagnetic field in a Frechet topology defined by local energy seminorms: this corresponds to the local energy decay. We then introduce the set of stationary states for the Landau--Lifschitz--Gilbert equation and prove that it corresponds to the attractor set for the distribution of magnetization whose presence is one of the characteristics of ferromagnetic media.