TY  - JOUR
A1  - Harris, Isaac
A1  - Kleefeld, Andreas
T1  - Analysis and computation of the transmission eigenvalues with a conductive boundary condition
T2  - Applicable Analysis
N2  - We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber–Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown.
KW  - Boundary integral equations
KW  - Inverse spectral problem
KW  - Conductive boundary condition
KW  - Transmission eigenvalues
Y1  - 2020
UR  - https://opus.bibliothek.fh-aachen.de/opus4/frontdoor/index/index/docId/11488
SN  - 1563-504X
VL  - 101
IS  - 6
SP  - 1880
EP  - 1895
PB  - Taylor & Francis
CY  - London
ER  -