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Relaxed model for the hysteresis in micromagnetism

Published online by Cambridge University Press:  08 July 2009

G. Carbou ,
M. A. Efendiev  and
P. Fabrie
G. Carbou
Affiliation:
Institut de Mathématiques de Bordeaux, UMR 5251, Université de Bordeaux, 351 cours de la Libération, 33405 Talence cedex, France (gilles.carbou@math.u-bordeaux.fr)
M. A. Efendiev
Affiliation:
Institute of Biomathematics and Biometry, Helmholtz Zentrum München, Ingolstädter Landstrasse 1, 85764 Neuherberg, Germany (messoud.efendiev@helmholtz-muenchen.de)
P. Fabrie
Affiliation:
Institut de Mathématiques de Bordeaux, UMR 5251, Université de Bordeaux, 351 cours de la Libération, 33405 Talence cedex, France (pierre.fabrie@math.u-bordeaux.fr)
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Abstract

We study a model of ferromagnetic material with hysteresis effects. The magnetic moment behaviour is described by the nonlinear Landau–Lifshitz 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 4 , August 2009 , pp. 759 - 773
Copyright
Copyright © Royal Society of Edinburgh 2009

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