TY  - JOUR
AU  - Harris, Isaac
AU  - Kleefeld, Andreas
TI  - Analysis and computation of the transmission eigenvalues with a conductive boundary condition
JO  - Applicable analysis
VL  - 101
IS  - 6
SN  - 1026-7360
M1  - FZJ-2020-02436
SP  - 1880-1895
PY  - 2022
AB  - We provide a new analytical and computational study of the transmission eigenvalueswith a conductive boundary condition. These eigenvalues are derived fromthe scalar inverse scattering problem for an inhomogeneous material with a conductiveboundary condition. The goal is to study how these eigenvalues depend onthe material parameters in order to estimate the refractive index. The analyticalquestions we study are: deriving Faber-Krahn type lower bounds, the discretenessand limiting behavior of the transmission eigenvalues as the conductivity tends toinfinity for a sign changing contrast. We also provide a numerical study of a newboundary integral equation for computing the eigenvalues. Lastly, using the limitingbehavior we will numerically estimate the refractive index from the eigenvaluesprovided the conductivity is sufficiently large but unknown.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000547422000001
DO  - DOI:10.1080/00036811.2020.1789598
UR  - https://juser.fz-juelich.de/record/877748
ER  -