Stability of thin layer approximation of electromagnetic waves scattering by linear and nonlinear coatings

We consider first the scattering problem of electromagnetic waves by thin coatings that are formed by linear materials. We describe, through an asymptotic study, the formal derivation of thin layer approximations, called effective boundary conditions. We then discuss the stability in time of the new initial boundary value problems. We give in the last part a generalization to nonlinear coatings of ferromagnetic type.