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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 12, Pages 7–16 (Mi ivm1456)  
This article is cited in 3 scientific papers (total in 3 papers)

Singularly perturbed Dirichlet boundary value problem for a stationary system in the linear elasticity theory

D. B. Davletov

Bashkir State University of Liberal Arts, Ufa
Full-text PDF (204 kB) Citations (3)
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Abstract: We consider a singularly perturbed Dirichlet boundary value problem for an elliptic operator of the linear elasticity theory in a bounded domain with a small cavity. The main result is the proof of the theorem about the convergence of eigenelements of the perturbed boundary value problem to eigenelements of the corresponding limit boundary value problem, when the parameter $\varepsilon$ which defines the diameter of the small cavity tends to zero.
Keywords: operator, boundary value problem, singular perturbation, eigenelements.
Received: 17.10.2006
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, Volume 52, Issue 12, Pages 4–12
DOI: https://doi.org/10.3103/S1066369X08120025
Bibliographic databases:
UDC: 517.956
Language: Russian
Citation: D. B. Davletov, “Singularly perturbed Dirichlet boundary value problem for a stationary system in the linear elasticity theory”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 12, 7–16; Russian Math. (Iz. VUZ), 52:12 (2008), 4–12
Citation in format AMSBIB
\Bibitem{Dav08}
\by D.~B.~Davletov
\paper Singularly perturbed Dirichlet boundary value problem for a stationary system in the linear elasticity theory
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 12
\pages 7--16
\mathnet{http://mi.mathnet.ru/ivm1456}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2530552}
\zmath{https://zbmath.org/?q=an:1167.35341}
\elib{https://elibrary.ru/item.asp?id=11592107}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 12
\pages 4--12
\crossref{https://doi.org/10.3103/S1066369X08120025}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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