Identification of generalized impedance boundary conditions in inverse scattering problemsReport as inadecuate




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1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231 2 DeFI - Shape reconstruction and identification CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641

Abstract : In the context of scattering problems in the harmonic regime, we consider the problem of identification of some Generalized Impedance Boundary Conditions GIBC at the boundary of an object which is supposed to be known from far field measurements associated with a single incident plane wave at a fixed frequency. The GIBCs can be seen as approximate models for thin coatings, corrugated surfaces or highly absorbing media. After pointing out that uniqueness does not hold in the general case, we propose some additional assumptions for which uniqueness can be restored. We also consider the question of stability when uniqueness holds. We prove in particular Lipschitz stability when the impedance parameters belong to a compact set. We also extend local stability results to the case of back-scattering data.

Keywords : Inverse scattering problems in electromagnetism and acoustics generalized impedance boundary conditions stability





Author: Laurent Bourgeois - Houssem Haddar -

Source: https://hal.archives-ouvertes.fr/



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