Asymptotic expansion of transmission eigenvalues for anisotropic thin layers
APPLICABLE ANALYSIS(2024)
Abstract
We study the asymptotic expansion of transmission eigenvalues for anisotropic thin layers. We establish a rigorous second-order expansion for simple transmission eigenvalues with respect to the thickness of the layer. The convergence analysis is based on a generalization of Osborn's Theorem to non-linear eigenvalue problems by Moskow [Nonlinear eigenvalue approximation for compact operators. J Math Phys. 2015;56(11):113512]. We also provide formal derivation in more general cases validating the obtained theoretical result.
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Key words
Transmission eigenvalues,asymptotic expansions,anisotropic thin layers
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