Maxwell's Equations in a 1D Ferromagnetic Medium : Existence and Uniqueness of Strong Solutions

Patrick Joly 1 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 are interested in the Maxwell's equations together with the Landau-Lifchitz-Gilbert law in order to model absorbing ferromagnetic materials in 1D. Using a fixed point theorem we establish existence and uniqueness of strong global solutions in suitable spaces, namely $\hrotr$ for the electric and magnetic fields $\eg$ and $\hg$, and $\ldlic$ for the magnetization $\mg$.
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Patrick Joly, Olivier Vacus. Maxwell's Equations in a 1D Ferromagnetic Medium : Existence and Uniqueness of Strong Solutions. [Research Report] RR-3052, INRIA. 1996. ⟨inria-00073640⟩

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