Decay rates for solutions of a Maxwell system with nonlinear boundary damping

The purpose of this paper is to obtain decay rates for the electromagnetic energy of solutions of a dynamic Maxwell system with spatially varying dielectric constant epsilon and magnetic permeability mu in a bounded, connected domain Omega. Dissipation is introduced into the system through a nonlinear Silver-Muller boundary condition. A general result on energy decay is proved when partial derivative Omega is an element of C-infinity and consists of a single connected component, and epsilon, mu are of class C-infinity((Omega) over bar) and satisfy a certain technical condition. Examples are provided that illustrate the general result and, in particular, it is shown how dissipative boundary conditions may be constructed that lead to a specified energy decay rate.