Mathematical analysis of high frequency pulse propagation in nonlinear dielectric materials

We consider high frequency electromagnetic pulse propagation in complex nonlinear dielectric materials. The physical problem is modeled by a Maxwell system which is then reduced to the specific problem. The nonlinear properties of the material are accounted for by using a nonlinear Debye model for the polarization. We use a Galerkin method to establish existence, uniqueness and continuous dependence of the resulting system.