Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Stability for static walls in ferromagnetic nanowires

Pages: 273 - 290, Volume 6, Issue 2, March 2006      doi:10.3934/dcdsb.2006.6.273

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Gilles Carbou - MAB, Université Bordeaux 1, 351, cours de la Libration, 33405 Talence cedex, France (email)
Stéphane Labbé - Laboratoire de Mathématique, Bât. 425, Université Paris 11, 91405 Orsay cedex, France (email)

Abstract: 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.

Keywords:  Stability, Non-Linear PDE, Micromagnetism.
Mathematics Subject Classification:  Primary: 34D10, 34D05; Secondary: 35K55.

Received: January 2005;      Revised: August 2005;      Available Online: December 2005.