Geodesic
Weak solutions to the Landau-Lifshitz-Maxwell system with nonlinear Neumann boundary conditions arising from surface energies
Electronic Journal of Differential Equations, Tome 2015 (2015).

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Summary: 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.
Classification : 35D30, 35F31, 35Q61
Keywords: ferromagnetism, micromagnetism, surface energy, Landau-Lifshitz-Maxwell equation, nonlinear PDE 
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     author = {Carbou, Gilles and Fabrie, Pierre and Santugini, K\'evin},
     title = {Weak solutions to the {Landau-Lifshitz-Maxwell} system with nonlinear {Neumann} boundary conditions arising from surface energies},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a4/}
}
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Carbou, Gilles; Fabrie, Pierre; Santugini, Kévin. Weak solutions to the Landau-Lifshitz-Maxwell system with nonlinear Neumann boundary conditions arising from surface energies. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a4/