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 Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 10, Pages 1847–1858 (Mi zvmmf99)

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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:10, 1811–1822

Bibliographic databases:

UDC: 519.632.4

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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\paper Asymptotics of eigenvalues of the Dirichlet boundary value problem for the Lame operator in a~three-dimensional domain with a~small cavity
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 10
\pages 1847--1858
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\transl
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 10
\pages 1811--1822
\crossref{https://doi.org/10.1134/S0965542508100072}
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• http://mi.mathnet.ru/eng/zvmmf/v48/i10/p1847

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. D. B. Davletov, “Asymptotics of Eigenvalues of the Two-Dimensional Dirichlet Boundary-Value Problem for the Lamé Operator in a Domain with a Small Hole”, Math. Notes, 93:4 (2013), 545–555
2. D. B. Davletov, D. V. Kozhevnikov, “The problem of Steklov type in a half-cylinder with a small cavity”, Ufa Math. J., 8:4 (2016), 62–87
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