Analysis of the transmission eigenvalue problem with two conductivity parameters

ABSTRACT

In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.

KEYWORDS:

• Transmission Eigenvalues
• Conductive Boundary Condition
• Inverse Scattering

AMS SUBJECT CLASSIFICATIONS:

• 35J05
• 35J35
• 78M15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of R. Ceja Ayala and I. Harris is partially supported by the NSF DMS Grant [grant number 2107891].