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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
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.
Received: 21.03.2017 Revised: 23.02.2018
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
Linking options:
https://www.mathnet.ru/eng/im8674https://doi.org/10.1070/IM8674 https://www.mathnet.ru/eng/im/v82/i6/p37
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Abstract page: | 442 | Russian version PDF: | 59 | English version PDF: | 33 | References: | 51 | First page: | 37 |
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