Asymptotic analysis of the transmission eigenvalue problem for a Dirichlet obstacle coated by a thin layer of non-absorbing media

Fioralba Cakoni 1 Houssem Haddar 2 Nicolas Chaulet 2
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first transmission eigenvalue with respect to the thickness of the thin layer. Our convergence analysis is based on a Max–Min principle and an iterative approach which involves estimates on the corresponding eigenfunctions. We provide explicit expressions for the terms in the asymptotic expansion up to order 3.
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Submitted on : Tuesday, January 27, 2015 - 11:44:36 AM
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Fioralba Cakoni, Houssem Haddar, Nicolas Chaulet. Asymptotic analysis of the transmission eigenvalue problem for a Dirichlet obstacle coated by a thin layer of non-absorbing media. IMA Journal of Applied Mathematics, Oxford University Press (OUP), 2014, pp.36. ⟨10.1093/imamat/hxu045⟩. ⟨hal-01109975⟩

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