Eigenfunctions localised on a defect in high-contrast random media

Capoferri, Matteo, Cherdantsev, Mikhail ORCID: https://orcid.org/0000-0002-5175-5767 and Velčić, Igor 2023. Eigenfunctions localised on a defect in high-contrast random media. SIAM Journal on Mathematical Analysis 55 (6) 10.1137/21M1468486

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Abstract

We study the properties of eigenvalues and corresponding eigenfunctions generated by a defect in the gaps of the spectrum of a high-contrast random operator. We consider a family of elliptic operators in divergence form whose coefficients are random, possess double porosity type scaling, and are perturbed on a fixed-size compact domain (a defect). Working in the gaps of the limiting spectrum of the unperturbed operator , we show that the point spectrum of converges in the sense of Hausdorff to the point spectrum of the limiting two-scale operator as . Furthermore, we prove that the eigenfunctions of decay exponentially at infinity uniformly for sufficiently small . This, in turn, yields strong stochastic two-scale convergence of such eigenfunctions to eigenfunctions of .

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	0036-1410
Date of First Compliant Deposit:	26 July 2023
Date of Acceptance:	10 July 2023
Last Modified:	15 Nov 2024 00:15
URI:	https://orca.cardiff.ac.uk/id/eprint/161272

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