The three dimensional Maxwell equations with strongly anisotropic electric permittivity

Abstract

The subject matter of this work concerns the propagation of the electro-magnetic fields through strongly anisotropic media, in the three dimensional setting. We concentrate on the asymptotic behavior for the solutions of the Maxwell equations when the electric permittivity tensor is strongly anisotropic. We derive limit models and prove their well-posedness. We appeal to the variational framework and study the propagation speed of the solutions. We prove that almost all the electro-magnetic energy concentrates inside the propagation cone of the limit model.