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Izvestiya: Mathematics, 2018, Volume 82, Issue 6, Pages 1108–1135
DOI: https://doi.org/10.1070/IM8674 (Mi im8674) 		 
This article is cited in 11 scientific papers (total in 11 papers)

On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type

R. R. Gadyl'shinab, A. L. Piatnitskicd, G. A. Chechkine

a Bashkir State Pedagogical University, Ufa
b Bashkir State University, Ufa
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
d The Arctic University of Norway, Narvik, Norway
e Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (422 kB) Citations (11)
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DOI: https://doi.org/10.1070/IM8674
Abstract: We consider a two-dimensional spectral problem of Steklov type for the Laplace operator in a domain divided into two parts by a perforated partition with a periodic microstructure. The Steklov boundary condition is imposed on the lateral sides of the perforation, the Neumann condition on the remaining part of the boundary, and the Dirichlet and Neumann conditions on the outer boundary of the domain. We construct and justify two-term asymptotic expressions for the eigenvalues of this problem. We also construct a two-term asymptotic formula for the corresponding eigenfunctions.
Keywords: asymptotic behaviour of eigenvalues, spectral problem, Steklov problem, homogenization of spectral problems.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00046
The investigation of the third author was carried out with the support of the Russian Foundation for Basic Research (grant no. 18-01-00046).
Received: 21.03.2017
Revised: 23.02.2018
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2018, Volume 82, Issue 6, Pages 37–64
DOI: https://doi.org/10.4213/im8674
Bibliographic databases:
Document Type: Article
UDC: 517.956.226
MSC: Primary 35B27; Secondary 35C20, 35J05, 35J25
Language: English
Original paper language: Russian
Citation: R. R. Gadyl'shin, A. L. Piatnitski, G. A. Chechkin, “On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type”, Izv. RAN. Ser. Mat., 82:6 (2018), 37–64; Izv. Math., 82:6 (2018), 1108–1135
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:442
    Russian version PDF:59
    English version PDF:33
    References:51
    First page:37
     
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