On the ferromagnetism equations with large variations solutions

We exhibit some large variations solutions of the Landau-Lifschitz equations as the exchange coefficient ε^2 tends to zero. These solutions are described by some asymptotic expansions which involve some internals layers by means of some large amplitude fluctuations in a neighborhood of width of order ε of an hypersurface contained in the domain. Despite the nonlinear behaviour of these layers we manage to justify locally in time these asymptotic expansions