论文标题
通过两个电导率参数分析传输特征值问题
Analysis of the transmission eigenvalue problem with two conductivity parameters
论文作者
论文摘要
在本文中，我们提供了两个电导率参数的传输特征值问题的分析研究。我们将假设潜在的物理模型是通过平面波的散射给出了各向同性散射器的。在先前的研究中，用一个导电边界参数分析了这个特征值问题，而我们将考虑两个参数的情况。我们将证明传输特征值的存在和离散性以及研究对物理参数的依赖性。我们能够证明第一个传输特征值相对于参数的单调性，并将限制过程视为第二个边界参数消失。最后，我们提供了广泛的数值实验来验证理论工作。
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 will 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.
