The Asymptotic of Transmission Eigenvalues for a Domain with a Thin Coating

Hanen Boujlida 1 Houssem Haddar 2 Moez Khenissi 1
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 a medium surrounded by a thin layer of inhomogeneous material with different refractive index. We derive explicit asymptotic expansion for the transmission eigenvalues with respect to the thickness of the thin layer. We prove error estimate for the asymptotic expansion up to order 1 for simple eigenvalues. This expansion can be used to obtain explicit expressions for constant index of refraction.
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Submitted on : Monday, December 3, 2018 - 9:52:03 PM
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Hanen Boujlida, Houssem Haddar, Moez Khenissi. The Asymptotic of Transmission Eigenvalues for a Domain with a Thin Coating. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2018, 78 (5), pp.2348-2369. ⟨hal-01646003v2⟩

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