ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF THE MAXWELL SYSTEM IN THE PRESENCE OF SMALL CHANGES IN THE INTERFACE OF AN INCLUSION

Abdessatar Khelifi; Siwar Saidani

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ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF THE MAXWELL SYSTEM IN THE PRESENCE OF SMALL CHANGES IN THE INTERFACE OF AN INCLUSION

机译：ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF THE MAXWELL SYSTEM IN THE PRESENCE OF SMALL CHANGES IN THE INTERFACE OF AN INCLUSION

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摘要

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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《Communications on pure and applied analysis》 |2022年第9期|2891-2909|共19页
作者
Abdessatar Khelifi; Siwar Saidani;
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作者单位

Department of Mathematics, Faculty of Sciences of Bizerte University of Carthage, Tunisia;

GAMA Laboratory LR21ES10 Faculty of Sciences of Bizerte, 7021 Zarzouna, Bizerte University of Carthage, Tunisia;

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正文语种英语
中图分类数学;
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Eigenvalue; perturbation; Maxwell's equations; interface changes; asymptotic expansion;

ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF THE MAXWELL SYSTEM IN THE PRESENCE OF SMALL CHANGES IN THE INTERFACE OF AN INCLUSION

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