The interior transmission eigenvalue problem for an inhomogeneous media with a conductive boundary. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Bondarenko, O.; Harris, I.; Kleefeld, A.
• Is Part Of: Applicable analysis. Volume 96:Issue 1(2017)
• Page Start: 2
• Page End: 22
• Publication Date: 2017-01-02
• Subjects: Inverse scattering -- inhomogeneous medium -- transmission eigenvalues -- inverse spectral problem -- conductive boundary condition; 35P25 -- 35P30 -- 35J30 -- 78A46; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1204440
• Languages: English
• ISSNs: 0003-6811

Abstract

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 n and boundary conductivity parameter, and obtain a uniqueness result for constant coefficients. We provide some numerical examples to demonstrate the theoretical results in three dimensions.