The three dimensional Maxwell equations with strongly anisotropic electric permittivity

Article type: Research Article

Authors: Bostan, Mihaï^{; *}

Affiliations: Aix Marseille Université, CNRS, Centrale Marseille, Institut de Mathématiques de Marseille, UMR 7373, Château Gombert 39 rue F. Joliot Curie, 13453 Marseille, France. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

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.

Keywords: Maxwell equations, evolution second order problems, variational solutions, asymptotic behavior

DOI: 10.3233/ASY-211730

Journal: Asymptotic Analysis, vol. 129, no. 3-4, pp. 289-320, 2022