Volume 50, Number 3, May-June 2016Special Issue – Polyhedral discretization for PDE
|Page(s)||905 - 920|
|Published online||23 May 2016|
The electromagnetic scattering problem with generalized impedance boundary conditions
Department of Mathematics, University College
London, Gower street,
London, WC1E 6BT, UK
Received: 18 November 2013
Revised: 24 November 2014
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.
Mathematics Subject Classification: 35P25 / 35G05 / 35Q61 / 78A45
Key words: Maxwell’s equations / generalized impedance boundary conditions / electromagnetic scattering / Helmholtz’ decomposition
© EDP Sciences, SMAI 2016
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