关于电磁散射理论中透射特征值的注记

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI:10.3934/IPI.2021025

F. Cakoni, S. Meng, Jingni Xiao

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引用次数: 2

摘要

这篇短文的动机是我们努力研究麦克斯韦方程组是否存在一个没有透射本征值的半平面。这一问题涉及时域内传输问题的可解性，而时域内传输问题的可解性对时变数据的线性采样和因式分解方法的正确性起着至关重要的作用。我们最初的目标是采用[21,23]中开发的半经典分析技术来证明，对于某些电磁参数组合，传输特征值位于围绕实轴的条带中。不幸的是，我们失败了。为了理解其中的原因，我们研究了球对称介质的特殊例子，这为我们提供了一些关于为什么我们不能证明上述结果的见解。因此，本文报道了我们关于球层介质麦克斯韦方程组的所有传输特征值的位置和复传输特征值的存在性的发现。我们希望这些结果可以为一般的电磁介质提供合理的推测。

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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A note on transmission eigenvalues in electromagnetic scattering theory

This short note was motivated by our efforts to investigate whether there exists a half plane free of transmission eigenvalues for Maxwell's equations. This question is related to solvability of the time domain interior transmission problem which plays a fundamental role in the justification of linear sampling and factorization methods with time dependent data. Our original goal was to adapt semiclassical analysis techniques developed in [21,23] to prove that for some combination of electromagnetic parameters, the transmission eigenvalues lie in a strip around the real axis. Unfortunately we failed. To try to understand why, we looked at the particular example of spherically symmetric media, which provided us with some insight on why we couldn't prove the above result. Hence this paper reports our findings on the location of all transmission eigenvalues and the existence of complex transmission eigenvalues for Maxwell's equations for spherically stratified media. We hope that these results can provide reasonable conjectures for general electromagnetic media.

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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.