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Eurasian Mathematical Journal, 2015, Volume 6, Number 3, Pages 13–29 (Mi emj199)  

This article is cited in 3 scientific papers (total in 3 papers)

Degeneration of Steklov–type boundary conditions in one spectral homogenization problem

A. G. Chechkina, V. A. Sadovnichy

Department of Mathematical Analysis, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, 1 Leninskie Gory, Moscow 119991, Russia
Full-text PDF (797 kB) Citations (3)
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Abstract: We consider a singularly perturbed Steklov–type problem for the second order linear elliptic equation in a bounded two–dimensional domain. We assume that the Steklov spectral condition rapidly alternates with the homogeneous Dirichlet condition on the boundary. The alternating parts of the boundary with the Dirichlet and Steklov conditions have the same small length of order $\varepsilon$. It is proved that when the small parameter tends to zero the eigenvalues of this problem degenerate, i.e. they tend to infinity. Moreover, it is proved that the eigenvalues of the initial problem are of order $\varepsilon^{-1}$ when $\varepsilon$ tends to zero.
Keywords and phrases: spectral problem, Steklov–type boundary condition, homogenization, rapidly alternating boundary condition, singular perturbation, estimate of convergence.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation ÍØ-7461.2016.1
The paper was partially supported by the program “Leading Scientific Schools” (project HØ-7461.2016.1).
Received: 20.11.2014
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. G. Chechkina, V. A. Sadovnichy, “Degeneration of Steklov–type boundary conditions in one spectral homogenization problem”, Eurasian Math. J., 6:3 (2015), 13–29
Citation in format AMSBIB
\Bibitem{CheSad15}
\by A.~G.~Chechkina, V.~A.~Sadovnichy
\paper Degeneration of Steklov–type boundary conditions in one spectral homogenization problem
\jour Eurasian Math. J.
\yr 2015
\vol 6
\issue 3
\pages 13--29
\mathnet{http://mi.mathnet.ru/emj199}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000374499900002}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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