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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 23, Issue 4


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

Andreas Kirsch / Hayk Asatryan
Published Online: 2014-12-04 | DOI: https://doi.org/10.1515/jiip-2014-0021


We 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.

Keywords: Helmholtz equation; transmission eigenvalues; Liouville transform; asymptotics of eigenvalues

MSC: 35P99; 34L05; 34L20

About the article

Received: 2014-03-05

Accepted: 2014-09-11

Published Online: 2014-12-04

Published in Print: 2015-08-01

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 23, Issue 4, Pages 299–307, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2014-0021.

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