Stochastic homogenization of the Landau-Lifshitz-Gilbert equation

Following the ideas of Zhikov and Piatnitski (Izv Math 70(1):19-67, 2006), 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-Gilbert equation. These equations have strong nonlinear features, and in general their solutions are not unique.

Automated summary

This paper establishes a homogenization theorem in a stochastic setting for two nonlinear equations, the equation of harmonic maps and the Landau-Lifschitz-Gilbert equation, based on the ideas of Zhikov and Piatnitski. These equations have strong nonlinear features and generally do not have unique solutions.