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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 1, Pages 102–115 (Mi zvmmf537)  
This article is cited in 31 scientific papers (total in 31 papers)

Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with oscillating boundary

Y. Amirata, G. A. Chechkinb, R. R. Gadyl'shincd

a Laboratoire de Mathématiques, Université Blaise Pascal, CNRS UMR 6620, 63177 Aubière cedex, France
b Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia
c Department of Mathematical Analysis, Faculty of Physics and Mathematics, Bashkir State Pedagogical University, Ufa, 450000, Russia
d Institute of Mathematics (with Computing Center), Russian Academy of Sciences, Ufa, 450077, Russia
Full-text PDF (1483 kB) Citations (31)
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Abstract: The asymptotic behavior of solutions to spectral problems for the Laplace operator in a domain with a rapidly oscillating boundary is analyzed. The leading terms of the asymptotic expansions for eigenelements are constructed, and the asymptotics are substantiated for simple eigenvalues.
Key words: oscillating boundary, spectrum of the Laplacian, asymptotics, matching of asymptotic expansions.
Received: 07.06.2005
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 1, Pages 97–110
DOI: https://doi.org/10.1134/S0965542506010118
Bibliographic databases:
Document Type: Article
UDC: 519.632.4
Language: English
Citation: Y. Amirat, G. A. Chechkin, R. R. Gadyl'shin, “Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with oscillating boundary”, Zh. Vychisl. Mat. Mat. Fiz., 46:1 (2006), 102–115; Comput. Math. Math. Phys., 46:1 (2006), 97–110
Citation in format AMSBIB
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\by Y.~Amirat, G.~A.~Chechkin, R.~R.~Gadyl'shin
\paper Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a~domain with oscillating boundary
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 1
\pages 102--115
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2239730}
\zmath{https://zbmath.org/?q=an:05200890}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 1
\pages 97--110
\crossref{https://doi.org/10.1134/S0965542506010118}
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    • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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