Approximate impedance for time-harmonic Maxwell's equations in a non planar domain with contrasted multi-thin layers

The aim of this paper is to give asymptotic models for the impedance of contrasted multi-thin layers for the harmonic Maxwell's equations. We start from a transmission problem which describes the scattering of electromagnetic waves by an obstacle covered with a thin coating (superposition of different thin layers of dielectric materials). We show how to model the effect of the thin coating by an impedance boundary condition on the boundary of the propagation domain. To this end, we use a technique of abstract differential equations.