Ferrornagnets with biquadratic exchange coupling energy. Global existence of weak solutions

摘要

A global existence theorem is proved for the Landau-Lifshitz-Gilbert equations with biquadratic exchange coupling energy acting on the interfaces of a material composed by two ferromagnetic layers separated by a nonmagnetic one. This energy is not convex. The magnetization M satisfies on the interfaces a coupled non-linear Neumann boundary condition with cubic growth. We use several regularizations, in particular for the traces of the magnetization at the interfaces, to obtain global weak solutions of the problem with finite energy. Copyright (c) 2005 John Wiley & Sons, Ltd.