Asymptotics of eigenvalues of the Maxwell system in a domain with small cavities

Korikov, D.

doi:10.1090/spmj/1582

Asymptotics of eigenvalues of the Maxwell system in a domain with small cavities
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by D. V. Korikov
Translated by: D. V. Korikov

St. Petersburg Math. J. 31 (2020), 13-51

DOI: https://doi.org/10.1090/spmj/1582

Published electronically: December 3, 2019

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Abstract:

The Maxwell system in a bounded domain $\Omega (\varepsilon )$ with finitely many cavities is considered. The cavity diameters are proportional to a small parameter $\varepsilon$. The perfect conductivity conditions are given on the boundary $\partial \Omega (\varepsilon )$. The asymptotics of the eigenvalues $\lambda (\varepsilon )$ is described as $\varepsilon \to 0$. The proposed model describes the perturbations of the eigenfrequencies of an electromagnetic resonator caused by the presence of metal particles in its volume; the model can be of use for plasma diagnostics.

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