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Eurasian Mathematical Journal, 2015, том 6, номер 3, страницы 13–29
(Mi emj199)
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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
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
Аннотация:
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.
Ключевые слова и фразы:
spectral problem, Steklov–type boundary condition, homogenization, rapidly alternating boundary condition, singular perturbation, estimate of convergence.
Поступила в редакцию: 20.11.2014
Образец цитирования:
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
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj199 https://www.mathnet.ru/rus/emj/v6/i3/p13
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Страница аннотации: | 355 | PDF полного текста: | 137 | Список литературы: | 96 |
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