The bottom of the spectrum in a double-contrast periodic model

N Babych

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A periodic spectral problem in a bounded domain with double inhomogeneities in mass density and stiffness coefficients is considered. A previous study [BKS08] has explored the problem by the method of asymptotic expansions with justification of errors showing that all eigenelements of the homogenized problem really approximate some of the perturbed eigenelements. Within this chapter additional results, partly announced in [BKS08], are obtained on the eigenfunction convergence at the bottom of the spectrum. It is shown that the eigenfunctions, which correspond to the eigenvalues at the bottom of the spectrum, could converge either to zero or to the eigenfunctions of the homogenized problem. The result was obtained by the method of two-scale convergence [Al92, Zh00].
Original languageEnglish
Title of host publicationIntegral Methods in Science and Engineering, Volume 1
Subtitle of host publicationAnalytic Methods
EditorsC Constanda, M E Perez
Place of PublicationBoston
PublisherBirkhauser
Pages53-63
Number of pages11
Volume1
ISBN (Electronic)9780817648992
ISBN (Print)9780817648985
DOIs
Publication statusPublished - 2010
Event10th International Conference on Integral Methods in Science and Engineering, IMSE 2008 - Santander, Spain
Duration: 7 Jul 201010 Jul 2010

Conference

Conference10th International Conference on Integral Methods in Science and Engineering, IMSE 2008
CountrySpain
CitySantander
Period7/07/1010/07/10

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Babych, N. (2010). The bottom of the spectrum in a double-contrast periodic model. In C. Constanda, & M. E. Perez (Eds.), Integral Methods in Science and Engineering, Volume 1: Analytic Methods (Vol. 1, pp. 53-63). Boston: Birkhauser. https://doi.org/10.1007/978-0-8176-4899-2-6