The interior transmission eigenvalue problem for an inhomogeneous media with a conductive boundary

TL;DR

This paper studies the interior transmission eigenvalue problem in inhomogeneous media with conductive boundaries, proving key properties, inverse spectral relations, and providing numerical demonstrations in three dimensions.

Contribution

It establishes the discreteness and existence of eigenvalues, analyzes their dependence on material parameters, and proves uniqueness results for constant coefficients.

Findings

Transmission eigenvalues are discrete and exist under given conditions.

The first eigenvalue varies monotonically with refractive index and boundary conductivity.

Numerical examples confirm theoretical results in three-dimensional settings.

Abstract

In this paper, we investigate the interior transmission eigenvalue problem for an inhomogeneous media with conductive boundary conditions. We prove the discreteness and existence of the transmission eigenvalues. We also investigate the inverse spectral problem of gaining information about the material properties from the transmission eigenvalues. In particular, we prove that the first transmission eigenvalue is a monotonic function of the refractive index and boundary conductivity parameter eta, and obtain a uniqueness result for constant coefficients. We provide some numerical examples to demonstrate the theoretical results in three dimensions