The interior transmission eigenvalue problem for elastic waves in media with obstacles

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI:10.3934/ipi.2020075

F. Cakoni, Pu-Zhao Kow, Jenn-Nan Wang

引用次数: 5

Abstract

In this paper, we investigate the interior transmission eigenvalue problem for elastic waves propagating outside a sound-soft or a sound-hard obstacle surrounded by an anisotropic layer. This study is motivated by the inverse problem of identifying an object embedded in an inhomogeneous media in the presence of elastic waves. Our analysis of this non-selfadjoint eigenvalue problem relies on the weak formulation of involved boundary value problems and some fundamental tools in functional analysis.

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有障碍物介质中弹性波的内部传播特征值问题

本文研究了在被各向异性层包围的声软或声硬障碍物外传播的弹性波的内部传输特征值问题。本研究的动机是识别在弹性波存在的非均匀介质中嵌入的物体的反问题。我们对这类非自伴随特征值问题的分析依赖于相关边值问题的弱表述和泛函分析中的一些基本工具。

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

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.