Spectral problem with Steklov condition on a thin perforated interface
- Authors: Gadyl’shin R.R.1,2, Piatnitski A.L.3,4, Chechkin G.A.5
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Affiliations:
- Bashkir State Pedagogical University
- Bashkir State University
- Narvik University College
- Lebedev Physical Institute
- Faculty of Mechanics and Mathematics
- Issue: Vol 93, No 1 (2016)
- Pages: 52-57
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223370
- DOI: https://doi.org/10.1134/S1064562416010191
- ID: 223370
Cite item
Abstract
A two-dimensional Steklov-type spectral problem for the Laplacian in a domain divided into two parts by a perforated interface with a periodic microstructure is considered. The Steklov boundary condition is set on the lateral sides of the channels, a Neumann condition is specified on the rest of the interface, and a Dirichlet and Neumann condition is set on the outer boundary of the domain. Two-term asymptotic expansions of the eigenvalues and the corresponding eigenfunctions of this spectral problem are constructed.
About the authors
R. R. Gadyl’shin
Bashkir State Pedagogical University; Bashkir State University
Author for correspondence.
Email: gadylshin@yandex.ru
Russian Federation, ul. Oktyabr’skoi revolyutsii 3a, Ufa, 450000; ul. Zaki Validi 32, Ufa, 450076
A. L. Piatnitski
Narvik University College; Lebedev Physical Institute
Email: gadylshin@yandex.ru
Norway, Narvik, 8505; Leninskii pr. 53, Moscow, 117924
G. A. Chechkin
Faculty of Mechanics and Mathematics
Email: gadylshin@yandex.ru
Russian Federation, Moscow, 119992