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We study a 2-scale version of the Landau-Lifshitz system of ferromagnetism,introduced by Starynkevitch to modelize hysteresis: the response of themagnetization is fast compared to a slowly varying applied magnetic fi eld.Taking the exchange term into account, in space dimension 3, we prove that,under some natural stability assumption on the equilibria of the system, thestrong solutions follow the dynamics of these equilibria. We also give explicitexamples of relevant equilibria and exterior magnetic fields, when theferromagnetic medium occupies some ellipsoidal domain.

Hysteresis for ferromagnetism: asymptotics of some 2-scale Landau-Lifshitz model