On Transitions to Stationary States in a Maxwell-Landau-Lifchitz-Gilbert SystemReport as inadecuate




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1 ONDES - Modeling, analysis and simulation of wave propagation phenomena Inria Paris-Rocquencourt, Univ. Paris-Saclay, ENSTA ParisTech - École Nationale Supérieure de Techniques Avancées, CNRS - Centre National de la Recherche Scientifique : UMR2706

Abstract : In this paper we consider Maxwell-s equations together with a dissipative non-linear magnetic law, the Landau-Lifchitz-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 electroma- gnetic field in a Fréchet topology defined by local energy seminorms: this corresponds to the local decay of energy. We then introduce that the set of stationary states for the Landau-Lifchitz-Gilbert equation and prove that it corresponds to the attractor set for the distribution of magnetizationwhose presence is one of the characteristics of ferromagnetic media.

Keywords : LIAPUNOV THEORY -LONG-TIME ASYMPTOTICS MAXWELL-S EQUATIONS LANDAU-LIFCHITZ-GILBERT LAW LOCAL DECAY OF ENERGY





Author: Patrick Joly - Alexander Komech Olivier Vacus -

Source: https://hal.archives-ouvertes.fr/



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