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Spectral asymptotics for a singularly perturbed fourth order locally periodic elliptic operator
Lomonosov Moscow State University, Moscow, Russia.
Narvik University College, Narvik, Norway.
Narvik University College, Narvik, Norway.
2015 (English)In: Asymptotic Analysis, ISSN 0921-7134, E-ISSN 1875-8576, Vol. 93, no 1-2, p. 141-160Article in journal (Refereed) Published
Abstract [en]

We consider the homogenization of a singularly perturbed self-adjoint fourth order elliptic operator with locally periodic coefficients, stated in a bounded domain. We impose Dirichlet boundary conditions on the boundary of the domain. The presence of large parameters in the lower order terms and the dependence of the coefficients on the slow variable lead to localization of the eigenfunctions. We show that the jth eigenfunction can be approximated by a rescaled function that is constructed in terms of the jth eigenfunction of fourth or second order effective operators with constant coefficients.

Place, publisher, year, edition, pages
2015. Vol. 93, no 1-2, p. 141-160
National Category
Mathematics
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URN: urn:nbn:se:hig:diva-27150DOI: 10.3233/ASY-151291OAI: oai:DiVA.org:hig-27150DiVA, id: diva2:1223097
Available from: 2018-06-25 Created: 2018-06-25 Last updated: 2018-06-25Bibliographically approved

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Pankratova, Iryna

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