On Transitions to Stationary States in a Maxwell-Landau-Lifchitz-Gilbert System

Patrick Joly 1 Alexander Komech Olivier Vacus 1
1 ONDES - Modeling, analysis and simulation of wave propagation phenomena
Inria Paris-Rocquencourt, UMA - Unité de Mathématiques Appliquées, 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.
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Patrick Joly, Alexander Komech, Olivier Vacus. On Transitions to Stationary States in a Maxwell-Landau-Lifchitz-Gilbert System. [Research Report] RR-3287, INRIA. 1997. ⟨inria-00073401⟩

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