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In this paper, we provide an analytical study of the transmission eigenvalueproblem with two conductivity parameters. We will assume that the underlyingphysical model is given by the scattering of a plane wave for an isotropicscatterer. In previous studies, this eigenvalue problem was analyzed with oneconductive boundary parameter whereas we will consider the case of twoparameters. We will prove the existence and discreteness of the transmissioneigenvalues as well as study the dependence on the physical parameters. We areable to prove monotonicity of the first transmission eigenvalue with respect tothe parameters and consider the limiting procedure as the second boundaryparameter vanishes. Lastly, we provide extensive numerical experiments tovalidate the theoretical work.

Analysis of the transmission eigenvalue problem with two conductivity parameters