Reconstruction of modified transmission eigenvalues using Cauchy data-Reference-Cited by-同舟云学术

Reconstruction of modified transmission eigenvalues using Cauchy data

Published:2023-04-26 Issue:6 Volume:31 Page:905-919
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Liu Juan¹,Liu Yanfang²,Sun Jiguang³^ORCID

Affiliation:

1. Department of Mathematics , Jinan University , Guangzhou , P. R. China

2. Department of Mathematics , The George Washington University , Washington D. C. , USA

3. Department of Mathematical Sciences , Michigan Technological University , Houghton , USA

Abstract

Abstract The modified transmission eigenvalue (MTE) problem was introduced in [S. Cogar, D. Colton, S. Meng and P. Monk, Modified transmission eigenvalues in inverse scattering theory, Inverse Problems 33 2017, 12, Article ID 125002] and used as a target signature for nondestructive testing. In this paper, we study the inverse spectral problem to reconstruct the modified transmission eigenvalues using Cauchy data. We propose a reciprocity gap functional method and show that the MTEs can be determined by solving some linear ill-posed integral equations. Numerical examples for both absorbing and non-absorbing media are presented to validate the effectiveness and robustness of the proposed method.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2022-0014/pdf

Reference19 articles.

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