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Matematicheskie Zametki, 2009, Volume 85, Issue 5, Pages 687–701
DOI: https://doi.org/10.4213/mzm3886
(Mi mzm3886)
 

This article is cited in 10 scientific papers (total in 10 papers)

Asymptotic Behavior of Eigenvalues of the Laplace Operator in Thin Infinite Tubes

V. V. Grushin

Moscow State Institute of Electronics and Mathematics
References:
Abstract: In this paper, we obtain an asymptotic expansion for the eigenvalues of the Laplace operator with zero Dirichlet conditions in tubes, i.e., in infinite bent cylinders with internal torsion under uniform contraction of their cross-sections, with respect to a small parameter characterizing the transverse dimensions of the tube. A method of reducing the problem of determining the eigenvalues to the solution of an implicit equation is proposed.
Keywords: eigenvalues of the Laplace operator, Dirichlet condition, thin infinite tube, Frenet equations, Schrödinger operator, Maslov canonical operator, quantum waveguide.
Received: 05.10.2006
English version:
Mathematical Notes, 2009, Volume 85, Issue 5, Pages 661–673
DOI: https://doi.org/10.1134/S000143460905006X
Bibliographic databases:
UDC: 517.958
Language: Russian
Citation: V. V. Grushin, “Asymptotic Behavior of Eigenvalues of the Laplace Operator in Thin Infinite Tubes”, Mat. Zametki, 85:5 (2009), 687–701; Math. Notes, 85:5 (2009), 661–673
Citation in format AMSBIB
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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