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On trajectories of complex-valued interior transmission eigenvalues

  • This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection.

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Author:Lukas Pieronek, Andreas KleefeldORCiD
ISSN:1930-8337 (Print)
ISSN:1930-8345 (Online)
Parent Title (English):Inverse problems and imaging : IPI
Place of publication:Springfield, Mo
Document Type:Article
Year of Completion:2024
Date of the Publication (Server):2024/04/09
Tag:Complex-valued eigenvalues; Eigenvalue trajectories; Interior transmission problem
First Page:480
Last Page:516
Institutes:FH Aachen / Fachbereich Medizintechnik und Technomathematik
collections:Verlag / AIMS