The interior transmission eigenvalue problem for a spherically-symmetric domain with anisotropic medium and a cavity

Abstract

AbstractWe consider the scattering of spherically-symmetric acoustic waves by an anisotropic medium and a cavity. While there is a large number of recent works devoted to the scattering problems with cavities, existence of an infinite set of transmission eigenvalues is an open problem in general. In this paper we prove existence of an infinite set of transmission eigenvalues for anisotropic Helmholtz and Schrödinger equations in a spherically-symmetric domain with a cavity. Further in this paper we consider the corresponding inverse problem. Under some assumptions we prove the uniqueness in the inverse problem.