Weak solutions to the Landau-Lifshitz-Maxwell system with nonlinear Neumann boundary conditions arising from surface energie

摘要

We study the Landau-Lifshitz system associated with Maxwell equations in abilayered ferromagnetic body when super-exchange and surface anisotropyinteractions are present in the spacer in-between the layers. In the presenceof these surface energies, the Neumann boundary condition becomes nonlinear. Weprove, in three dimensions, the existence of global weak solutions to theLandau-Lifshitz-Maxwell system with nonlinear Neumann boundary conditions.