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

This article is cited in 2 scientific papers (total in 2 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

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
Received: 14.01.2008

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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\jour Zh. Vychisl. Mat. Mat. Fiz.
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\pages 1847--1858
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\jour Comput. Math. Math. Phys.
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\pages 1811--1822
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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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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  mathnet  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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