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Composites with invisible inclusions: Eigenvalues of ℝ-linear problem

Published online by Cambridge University Press:  31 March 2016

V. V. MITYUSHEV
V. V. MITYUSHEV*
Affiliation:
Department of Computer Science and Computational Methods, Pedagogical University, Krakow, Poland e-mail: mityu@up.krakow.pl
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Abstract

A new eigenvalue ℝ-linear problem arisen in the theory of metamaterials and neutral inclusions is reduced to integral equations. The problem is constructively investigated for circular non-overlapping inclusions. An asymptotic formula for eigenvalues is deduced when the radii of inclusions tend to zero. The nodal domains conjecture related to univalent eigenfunctions is posed. Demonstration of the conjecture allows to justify that a set of inclusions can be made neutral by surrounding it with an appropriate coating.

Keywords

invisible inclusionsℝ-linear problemmetamaterialsunivalent eigenfunction

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 5 , October 2016 , pp. 796 - 806
Copyright
Copyright © Cambridge University Press 2016 

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