THE ANISOTROPIC INTERIOR TRANSMISSION EIGENVALUE PROBLEM WITH A CONDUCTIVE BOUNDARY
Document Type
Article
Publication Date
6-1-2025
Abstract
In this paper, we study the transmission eigenvalue problem for an anisotropic material with a conductive boundary. We prove that the transmission eigenvalues for this problem exist and are, at most, a discrete set. We also study the dependence of the transmission eigenvalues on the physical parameters and prove that the first transmission eigenvalue is monotonic. We then consider the limiting behavior of the transmission eigenvalues as the conductive boundary parameter η vanishes or goes to infinity in magnitude. Finally, we provide numerical examples on three domains to demonstrate our theoretical results.
Publication Title
Communications on Analysis and Computation
Recommended Citation
Hughes, V.,
Harris, I.,
&
Sun, J.
(2025).
THE ANISOTROPIC INTERIOR TRANSMISSION EIGENVALUE PROBLEM WITH A CONDUCTIVE BOUNDARY.
Communications on Analysis and Computation,
4, 60-82.
http://doi.org/10.3934/cac.2025007
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/2074