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

Hanen Boujlida (1) , Houssem Haddar (2) , Moez Khenissi (1)

1 ESSTHS - Ecole Supérieure des Sciences et de Technologie de Hammam Sousse
2 DeFI - Shape reconstruction and identification

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.

Mots clés: transmission eigenvalue; thin layer; inverse scattering.

Domaines: Analyse numérique [cs.NA]

Hanen Boujlida, Houssem Haddar, Moez Khenissi. The Asymptotic of Transmission Eigenvalues for a Domain with a Thin Coating. SIAM Journal on Applied Mathematics, 2018, 78 (5), pp.2348-2369. ⟨hal-01646003v2⟩