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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 10, Pages 1847–1858 (Mi zvmmf99)  
This article is cited in 4 scientific papers (total in 4 papers)

Asymptotics of eigenvalues of the Dirichlet boundary value problem for the Lame operator in a three-dimensional domain with a small cavity

D. B. Davletov

Bashkir State Pedagogical University, ul. Oktyabr'skoi revolyutsii 3a, Ufa, 450000, Bashkortostan, Russia
Full-text PDF (1055 kB) Citations (4)
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Abstract: A boundary value problem for the Lame operator in a bounded three-dimensional domain with a small cavity is studied. The domain is filled with an elastic homogeneous isotropic medium that is clamped at the boundary, which corresponds to the Dirichlet boundary condition. The leading term of an asymptotic expansion for the eigenvalue is constructed in the case of the Dirichlet limit problem. The asymptotic expansion is constructed in powers of a small parameter $\varepsilon$ that is the diameter of the cavity.
Key words: Lame operator, boundary value problem, singular perturbation, eigenvalue and vector eigenfunction, asymptotic expansions.
Received: 14.01.2008
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 10, Pages 1811–1822
DOI: https://doi.org/10.1134/S0965542508100072
Bibliographic databases:
Document Type: Article
UDC: 519.632.4
Language: Russian
Citation: D. B. Davletov, “Asymptotics of eigenvalues of the Dirichlet boundary value problem for the Lame operator in a three-dimensional domain with a small cavity”, Zh. Vychisl. Mat. Mat. Fiz., 48:10 (2008), 1847–1858; Comput. Math. Math. Phys., 48:10 (2008), 1811–1822
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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