Analysis and computation of the transmission eigenvalues with a conductive boundary condition

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 eigenv...

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Bibliographic Details
Published in:Applicable analysis 2022-04, Vol.101 (6), p.1880-1895
Main Authors: Harris, I., Kleefeld, A.
Format: Article
Language:English
Subjects:
Boundary conditions
boundary integral equations
Boundary integral method
conductive boundary condition
Constraining
Eigenvalues
Integral equations
Inverse scattering
inverse spectral problem
Lower bounds
Refractivity
Transmission eigenvalues
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Summary: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.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2020.1789598