On trajectories of complex-valued interior transmission eigenvalues

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2023-01-01 DOI:10.3934/ipi.2023041

Lukas Pieronek, Andreas Kleefeld

引用次数: 0

Abstract

This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection.

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关于复值内传输特征值的轨迹

本文研究了利用折射率大小参数化的特征值轨迹的均匀介质内部传输问题。在散射体为单位圆盘的情况下，我们证明了复值内透射本征值轨迹与拉普拉斯函数的狄利克雷本征值之间存在一一对应关系，而狄利克雷本征值正是折射率趋于无穷大时的轨迹极限点。对于二维或三维的一般单连通散射体，其对应关系仍然是开放的，但进一步的理论结果和数值研究表明了类似的联系。

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.