Homogenization results for a Landau–Lifshitz–Gilbert equation in composite materials with transmission defects

Abstract

We study the homogenization of Landau–Lifshitz–Gilbert equation in a ϵ-periodic composite material formed by two constituents, separated by an imperfect interface , on which we prescribe the continuity of the conormal derivatives and a jump of the solution proportional to the conormal derivative, by means of a coefficient of order . We use the periodic unfolding method together with extension operators for handling the nonlinearities to identify the limit problem when tuning up the parameter γ in .