March  2006, 6(2): 273-290. doi: 10.3934/dcdsb.2006.6.273

Stability for static walls in ferromagnetic nanowires

1. 

MAB, Université Bordeaux 1, 351, cours de la Libration, 33405 Talence cedex, France

2. 

Laboratoire de Mathématique, Bât. 425, Université Paris 11, 91405 Orsay cedex, France

Received  January 2005 Revised  August 2005 Published  December 2005

The goal of this article is to analyze the time asymptotic stability of one dimensional Bloch walls in ferromagnetic materials. The equation involved in modelling such materials is the Landau-Lifchitz system which is non-linear and parabolic. We demonstrate that the equilibrium states called Bloch walls are asymptotically stable modulo a rotation and a translation transverse to the wall. The linear part of the perturbed equation admits zero as an eigenvalue forbidding a direct proof.
Citation: Gilles Carbou, Stéphane Labbé. Stability for static walls in ferromagnetic nanowires. Discrete & Continuous Dynamical Systems - B, 2006, 6 (2) : 273-290. doi: 10.3934/dcdsb.2006.6.273
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