Stabilization of heteregeneous Maxwell's equations by linear or nonlinear boundary feedbacks

We examine the question of stabilization of the (nonstationary) heteregeneous Maxwell's equations in a bounded region with a Lipschitz boundary by means of linear or nonlinear Silver-M"uller boundary condition. This requires the validity of some stability estimate in the linear case that may be checked in some particular situations. As a consequence we get an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks. Based on the linear stability estimate, we further obtain certain exact controllability results for the Maxwell system