Solutions to the Landau-Lifshitz system with nonhomogenous Neumann boundary conditions arising from surface anisotropy and super-exchange interactions in a ferromagnetic media

We study the solutions to the Landau-Lifshitz system in a bilayered ferromagnetic body when super-exchange and surface anisotropy interactions are present at the interface between the layers. We prove the existence of weak solutions in infinite time and strong solutions in finite time.