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)
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 
@article{EJDE_2015__2015__a4,
     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},
     year = {2015},
     volume = {2015},
     zbl = {1318.35113},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a4/}
}
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JO  - Electronic journal of differential equations
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%J Electronic journal of differential equations
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%F EJDE_2015__2015__a4
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/