Eigenfunctions localised on a defect in high-contrast random media
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| Titel: | Eigenfunctions localised on a defect in high-contrast random media |
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| Autoren: | Capoferri M., Cherdantsev M., Velcic I. |
| Weitere Verfasser: | M. Capoferri, M. Cherdantsev, I. Velcic |
| Verlagsinformationen: | Society for Industrial and Applied Mathematics Publications |
| Publikationsjahr: | 2023 |
| Bestand: | The University of Milan: Archivio Istituzionale della Ricerca (AIR) |
| Schlagwörter: | defect mode, high contrast media, localized eigenfunction, random media, stochastic homogenization, Settore MATH-03/A - Analisi matematica |
| Beschreibung: | 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 A ε 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 A widehat ε, we show that the point spectrum of A ε converges in the sense of Hausdorff to the point spectrum of the limiting two-scale operator A h o m as ε → 0. Furthermore, we prove that the eigenfunctions of A ε decay exponentially at infinity uniformly for sufficiently small ε. This, in turn, yields strong stochastic two-scale convergence of such eigenfunctions to eigenfunctions of A h o m . |
| Publikationsart: | article in journal/newspaper |
| Sprache: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/wos/WOS:001114759300032; volume:55; issue:6; firstpage:7449; lastpage:7489; numberofpages:41; journal:SIAM JOURNAL ON MATHEMATICAL ANALYSIS; https://hdl.handle.net/2434/1100992 |
| DOI: | 10.1137/21M1468486 |
| Verfügbarkeit: | https://hdl.handle.net/2434/1100992 https://doi.org/10.1137/21M1468486 |
| Rights: | info:eu-repo/semantics/openAccess |
| Dokumentencode: | edsbas.F04B6968 |
| Datenbank: | BASE |
Nájsť tento článok vo Web of Science | 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 A ε 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 A widehat ε, we show that the point spectrum of A ε converges in the sense of Hausdorff to the point spectrum of the limiting two-scale operator A h o m as ε → 0. Furthermore, we prove that the eigenfunctions of A ε decay exponentially at infinity uniformly for sufficiently small ε. This, in turn, yields strong stochastic two-scale convergence of such eigenfunctions to eigenfunctions of A h o m . |
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| DOI: | 10.1137/21M1468486 |