An identification problem for the Maxwell equations in a non-homogeneous dispersive medium

Abstract

We consider the propagation of electromagnetic waves in a non-homogeneous medium. The related constitutive relations contain time and space dependent convolution kernels. Since they are a priori unknown, a basic question concerns their identification. In the present paper, this is obtained by reducing the problem to a system of nonlinear integral equations of the second kind. Via a Contraction Theorem, we prove local (in time) existence and uniqueness results. Lipschitz continuous dependence upon the data is also proved.