The electromagnetic scattering problem with generalized impedance boundary conditions

Chaulet, Nicolas

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 3, pp. 905-920.

In this paper we consider the electromagnetic scattering problem by an obstacle characterised by a Generalized Impedance Boundary Condition in the harmonic regime. These boundary conditions are well known to provide accurate models for thin layers or imperfectly conducting bodies. We give two different formulations of the scattering problem and we provide some general assumptions on the boundary condition under which the scattering problem has at most one solution. We also prove that it is well-posed for three different boundary conditions which involve second order surface differential operators under weak sign assumptions on the coefficients defining the surface operators.

Classification : 35P25, 35G05, 35Q61, 78A45
Mots clés : Maxwell’s equations, generalized impedance boundary conditions, electromagnetic scattering, Helmholtz’ decomposition

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