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 .
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 Notice that the surface integrals make sense since is a Lipschitz surface.
2 The existence of follows from the Lax–Milgram theorem, see e.g. [Citation25]. See also [Citation22] for further results.