论文标题
具有导电边界条件的传输特征值的分析和计算
Analysis and computation of the transmission eigenvalues with a conductive boundary condition
论文作者
论文摘要
我们为具有导电边界条件的传输特征值提供了新的分析和计算研究。这些特征值来自具有导电边界条件的不均匀材料的标量反向散射问题。目的是研究这些特征值如何依赖材料参数，以估计折射率。我们研究的分析问题是：得出Faber-Krahn类型的下限，随着电导率倾向于无穷大，用于变化的对比度。我们还提供了用于计算特征值的新边界积分方程的数值研究。最后，使用限制行为，我们将在数值上估算特征值的折射率，前提是电导率足够大但未知。
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber-Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown.
