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Eurasian Mathematical Journal, 2015, Volume 6, Number 3, Pages 13–29
(Mi emj199)
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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
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.
Received: 20.11.2014
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
Linking options:
https://www.mathnet.ru/eng/emj199 https://www.mathnet.ru/eng/emj/v6/i3/p13
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Abstract page: | 361 | Full-text PDF : | 138 | References: | 97 |
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