The asymptotic of transmission eigenvalues for a domain with a thin coating

H. Boujlida; H. Haddar; M. Kheniss

doi:10.1137/17M1154126

The asymptotic of transmission eigenvalues for a domain with a thin coating

H. Boujlida, H. Haddar, M. Kheniss

Universit'e de Sousse

Research output: Contribution to journal › Article › peer-review

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 the error estimate for the asymptotic expansion up to order 1. This expansion can be used to obtain explicit expressions for a constant index of refraction.

Original language	English
Pages (from-to)	2348-2369
Number of pages	22
Journal	SIAM Journal on Applied Mathematics
Volume	78
Issue number	5
DOIs	https://doi.org/10.1137/17M1154126
Publication status	Published - 1 Jan 2018

Keywords

Asymptotic expansions
Inverse scattering problems
Thin layers
Transmission eigenvalues

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10.1137/17M1154126

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title = "The asymptotic of transmission eigenvalues for a domain with a thin coating",

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 the error estimate for the asymptotic expansion up to order 1. This expansion can be used to obtain explicit expressions for a constant index of refraction.",

keywords = "Asymptotic expansions, Inverse scattering problems, Thin layers, Transmission eigenvalues",

author = "H. Boujlida and H. Haddar and M. Kheniss",

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year = "2018",

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AU - Boujlida, H.

AU - Haddar, H.

AU - Kheniss, M.

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N2 - 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 the error estimate for the asymptotic expansion up to order 1. This expansion can be used to obtain explicit expressions for a constant index of refraction.

AB - 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 the error estimate for the asymptotic expansion up to order 1. This expansion can be used to obtain explicit expressions for a constant index of refraction.

KW - Asymptotic expansions

KW - Inverse scattering problems

KW - Thin layers

KW - Transmission eigenvalues

U2 - 10.1137/17M1154126

DO - 10.1137/17M1154126

M3 - Article

AN - SCOPUS:85055800893

SN - 0036-1399

VL - 78

SP - 2348

EP - 2369

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 5

ER -

The asymptotic of transmission eigenvalues for a domain with a thin coating

Abstract

Keywords

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