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Advances in Mathematical Physics
Volume 2016, Article ID 2438253, 9 pages
http://dx.doi.org/10.1155/2016/2438253
Research Article

Inverse Uniqueness in Interior Transmission Problem and Its Eigenvalue Tunneling in Simple Domain

Department of Mathematics, National Chung Cheng University, 168 University Road, Min-Hsiung, Chia-Yi County 621, Taiwan

Received 7 October 2015; Accepted 6 December 2015

Academic Editor: Ivan Avramidi

Copyright © 2016 Lung-Hui Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study inverse uniqueness with a knowledge of spectral data of an interior transmission problem in a penetrable simple domain. We expand the solution in a series of one-dimensional problems in the far-fields. We define an ODE by restricting the PDE along a fixed scattered direction. Accordingly, we obtain a Sturm-Liouville problem for each scattered direction. There exists the correspondence between the ODE spectrum and the PDE spectrum. We deduce the inverse uniqueness on the index of refraction from the discussion on the uniqueness anglewise of the Strum-Liouville problem.