TY  - JOUR
AU  - Pieronek, Lukas
AU  - Kleefeld, Andreas
TI  - On trajectories of complex-valued interior transmission eigenvalues
JO  - Inverse problems and imaging
VL  - 18
IS  - 2
SN  - 1930-8337
CY  - Springfield, Mo.
PB  - AIMS
M1  - FZJ-2024-03155
SP  - 480 - 516
PY  - 2024
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001072416100001
DO  - DOI:10.3934/ipi.2023041
UR  - https://juser.fz-juelich.de/record/1025792
ER  -