Extreme Localization of Eigenfunctions to One-Dimensional High-Contrast Periodic Problems with a Defect

DOI10.1137/17M112261XzbMath1409.34072arXiv1702.03538OpenAlexW2617086924MaRDI QIDQ4555740

Mikhail Cherdantsev, Shane Cooper, Kirill D. Cherednichenko

Publication date: 21 November 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.03538

zbMATH Keywords

spectrumdecay estimateswave localizationhigh-contrast homogenization

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) General spectral theory of ordinary differential operators (34L05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (7)

Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I ⋮ Asymptotic Analysis of Stratified Elastic Media in the Space of Functions with Bounded Deformation ⋮ Eigenfunctions Localised on a Defect in High-Contrast Random Media ⋮ Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate ⋮ Stochastic homogenisation of high-contrast media ⋮ Free, forced, and random vibrations of a beam composed of highly contrasting materials ⋮ Random response of multi-segment beam may exceed response of homogeneous counterparts by order of magnitude

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