Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation

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Publication details

JournalApplied Mathematics Research eXpress
DateE-pub ahead of print - 1 Apr 2012
DatePublished (current) - Apr 2012
Issue number1
Volume2013
Number of pages33
Pages (from-to)1-33
Early online date1/04/12
Original languageEnglish

Abstract

The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative space-dependent noise is considered for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere $\mathbb S^2$. The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert equation.

Bibliographical note

Appl Math Res Express first published online April 19, 2012

    Research areas

  • Landau-Lifshitz-Gilbert equation, , weak martingale solution, , Galerkin approx-imations, , compact embedding.

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