TY  - JOUR
A1  - Harris, Isaac
A1  - Kleefeld, Andreas
T1  - The inverse scattering problem for a conductive boundary condition and transmission eigenvalues
T2  - Applicable Analysis
N2  - In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside–outside duality method can be used to reconstruct the interior conductive eigenvalues.
KW  - Transmission eigenvalues
KW  - Conductive boundary condition
KW  - Inverse scattering
Y1  - 2024
UR  - https://opus.bibliothek.fh-aachen.de/opus4/frontdoor/index/index/docId/11471
SN  - 1563-504X
VL  - 99
IS  - 3
SP  - 508
EP  - 529
PB  - Taylor & Francis
CY  - London
ER  -