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

Abdessatar Khelifi; Siwar Saidani

doi:10.3934/cpaa.2022080

Article Contents

2022, Volume 21, Issue 9: 2891-2909. Doi: 10.3934/cpaa.2022080

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

Abdessatar Khelifi^1, , and
Siwar Saidani^2,

1.
Department of Mathematics, Faculty of Sciences of Bizerte, University of Carthage, Tunisia
2.
GAMA Laboratory LR21ES10, Faculty of Sciences of Bizerte, 7021 Zarzouna, Bizerte, University of Carthage, Tunisia

^*Corresponding author
^*Corresponding author

Received: June 2021

Revised: January 2022

Early access: April 2022

Published: September 2022

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Abstract

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 $ h $ 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.

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Mathematics Subject Classification: 35P15, 35Q60, 78M35.

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