The anisotropic interior transmission eigenvalue problem with a conductive boundary

In this paper, we study the transmission eigenvalue problem for an anisotropic material with a conductive boundary. We prove that the transmission eigenvalues for this problem exist and are, at most, a discrete set. We also study the dependence of the transmission eigenvalues on the physical parameters and prove that the first transmission eigenvalue is monotonic. We then consider the limiting behavior of the transmission eigenvalues as the conductive boundary parameter η vanishes or goes to infinity in magnitude. Finally, we provide numerical examples on three domains to demonstrate our theoretical results.