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Analysis of the transmission eigenvalue problem with two conductivity parameters

  • In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.

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Author:Rafael Ceja Ayala, Isaac HarrisORCiD, Andreas KleefeldORCiD, Nikolaos Pallikarakis
Parent Title (English):Applicable Analysis
Publisher:Taylor & Francis
Document Type:Article
Year of Completion:2023
Date of the Publication (Server):2023/03/07
Tag:Conductive Boundary Condition; Inverse Scattering; Transmission Eigenvalues
Length:37 Seiten
Institutes:FH Aachen / Fachbereich Medizintechnik und Technomathematik
collections:Verlag / Taylor & Francis