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.
DOI: 10.1051/m2an/2014064
Keywords: Maxwell’s equations, generalized impedance boundary conditions, electromagnetic scattering, Helmholtz’ decomposition
@article{M2AN_2016__50_3_905_0, author = {Chaulet, Nicolas}, title = {The electromagnetic scattering problem with generalized impedance boundary conditions}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {905--920}, publisher = {EDP-Sciences}, volume = {50}, number = {3}, year = {2016}, doi = {10.1051/m2an/2014064}, zbl = {1344.35073}, mrnumber = {3507278}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2014064/} }
TY - JOUR AU - Chaulet, Nicolas TI - The electromagnetic scattering problem with generalized impedance boundary conditions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 905 EP - 920 VL - 50 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014064/ DO - 10.1051/m2an/2014064 LA - en ID - M2AN_2016__50_3_905_0 ER -
%0 Journal Article %A Chaulet, Nicolas %T The electromagnetic scattering problem with generalized impedance boundary conditions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 905-920 %V 50 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014064/ %R 10.1051/m2an/2014064 %G en %F M2AN_2016__50_3_905_0
Chaulet, Nicolas. The electromagnetic scattering problem with generalized impedance boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 3, pp. 905-920. doi : 10.1051/m2an/2014064. http://www.numdam.org/articles/10.1051/m2an/2014064/
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