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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



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

Author: D. V. Korikov
Translated by: D. V. Korikov
Original publication: Algebra i Analiz, tom 31 (2019), nomer 1.
Journal: St. Petersburg Math. J. 31 (2020), 13-51
MSC (2010): Primary 35Q61
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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Additional Information

D. V. Korikov
Affiliation: St. Petersburg State University, Ul′yanova 1, 198504 St. Petersburg, Russia

Keywords: Maxwell system, singularly perturbed domains, asymptotics of eigenvalues
Received by editor(s): April 17, 2017
Published electronically: December 3, 2019
Additional Notes: The research was supported by Russian Science Foundation grant no. 17-11-01126
Article copyright: © Copyright 2019 American Mathematical Society