Reconstruction of modified transmission eigenvalues using Cauchy data

IF 1.2 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2023-04-26 DOI:10.1515/jiip-2022-0014

Juan Liu, Yanfang Liu, Jiguang Sun

引用次数: 0

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.

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利用柯西数据重构修正传输特征值

摘要[S.Cogar，D.Colton，S.Meng和P.Monk，逆散射理论中的修正透射本征值，逆问题33 2017，12，文章ID 125002]中介绍了修正透射本值（MTE）问题，并将其用作无损检测的目标签名。在本文中，我们研究了利用柯西数据重建修正透射本征值的逆谱问题。我们提出了一种互易间隙泛函方法，并证明了MTE可以通过求解一些线性不适定积分方程来确定。给出了吸收和非吸收介质的数值算例，验证了该方法的有效性和稳健性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography