Stochastic homogenization of the Landau-Lifshitz-Gilbert equation

2019/02/15 by Alouges, François, De Bouard, Anne, Merlet, Benoît +1
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1902.05743

Abstract

Following the ideas of V. V. Zhikov and A. L. Pyatnitski, and more precisely the stochastic two-scale convergence, this paper establishes a homogenization theorem in a stochastic setting for two nonlinear equations : the equation of harmonic maps into the sphere and the Landau-Lifschitz equation. These equations have strong nonlinear features, in particular, in general their solutions are not unique.

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• Numerical Homogenization of Landau-Lifshitz Equation with Rough Coefficients

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