Asymptotic behavior of eigenvalues of the Maxwell system in the presence of small changes in the interface of an inclusion

Abstract

<p style='text-indent:20px;'>In this paper, we derive rigorously asymptotic formulas for perturbations in the eigenfrequencies of a Maxwell system due to small changes in the interface of a smooth inclusion. Taking advantage of small perturbations, we use a rigorous asymptotic analysis to develop an asymptotic formula for the case where the eigenvalue of the reference problem is simple or multiple. We show that our asymptotic formulas can be expressed in terms of the electric permittivity and the profile function <inline-formula><tex-math id="M1">\begin{document}$ h $\end{document}</tex-math></inline-formula> modelling the shape perturbation. We assume that our results are ambitious tools to solve the inverse problem of identifying interface changes (deformations) of inclusions, given eigenvalues measurements.</p>