Analysis of the transmission eigenvalue problem with two conductivity parameters
Analysis of the transmission eigenvalue problem with two conductivity parameters
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DOI：
10.1080/00036811.2023.2181167
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发表时间：
2022-09
影响因子：
1.1
通讯作者：
R. Ayala;I. Harris;A. Kleefeld;Nikolaos Pallikarakis
中科院分区：
文献类型：
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作者：
R. Ayala;I. Harris;A. Kleefeld;Nikolaos Pallikarakis
本文对具有两个电导率参数的传输本征值问题进行了分析研究。我们假设基本的物理模型是由各向同性散射体的平面波散射给出的。在以前的研究中，这个特征值问题是用一个导电边界参数来分析的，而我们将考虑两个参数的情况。证明了传输本征值的存在性和离散性，并研究了传输本征值对物理参数的依赖关系。我们能够证明第一传输本征值关于参数的单调性，并考虑当第二边界参数为零时的极限过程。最后，我们提供了大量的数值实验来验证理论工作。
ABSTRACT In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.