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

Gilles Carbou (1) , Pierre Fabrie (2) , Kévin Santugini-Repiquet (2, 3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 IMB - Institut de Mathématiques de Bordeaux
3 MC2 - Modélisation, contrôle et calcul

We study the Landau-Lifshitz system associated with Maxwell equations in a bilayered ferromagnetic body when super-exchange and surface anisotropy interactions are present in the spacer in-between the layers. In the presence of these surface energies, the Neumann boundary condition becomes nonlinear. We prove, in three dimensions, the existence of global weak solutions to the Landau-Lifshitz-Maxwell system with nonlinear Neumann boundary conditions.

Domaines: Equations aux dérivées partielles [math.AP]

Gilles Carbou, Pierre Fabrie, Kévin Santugini-Repiquet. Weak solutions to the Landau-Lifshitz-Maxwell system with nonlinear Neumann boundary conditions arising from surface energie. Electronic Journal of Differential Equations, 2015. ⟨hal-00951318⟩