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Mat. Zametki, 2007, Volume 81, Issue 3, Pages 328–334 (Mi mz3675)  

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

Asymptotic Behavior of Eigenvalues of the Laplace Operator in Infinite Cylinders Perturbed by Transverse Extensions

V. V. Grushin

Moscow State Institute of Electronics and Mathematics

Abstract: We present sufficient conditions for the existence of an eigenvalue of the Laplace operator with zero Dirichlet conditions in a weakly perturbed infinite cylinder in the case of localized perturbations which are extensions along the transverse coordinates with coefficients depending on the longitudinal coordinate. If such an eigenvalue exists, then, for this eigenvalue, we obtain an asymptotic formula with respect to a small parameter characterizing the values of extensions.

Keywords: Laplace operator, eigenvalue, asymptotics, small parameter, infinite cylinder, localized perturbations

DOI: https://doi.org/10.4213/mzm3675

Full text: PDF file (445 kB)
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English version:
Mathematical Notes, 2007, 81:3, 291–296

Bibliographic databases:

UDC: 517.958
Received: 13.12.2005

Citation: V. V. Grushin, “Asymptotic Behavior of Eigenvalues of the Laplace Operator in Infinite Cylinders Perturbed by Transverse Extensions”, Mat. Zametki, 81:3 (2007), 328–334; Math. Notes, 81:3 (2007), 291–296

Citation in format AMSBIB
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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. V. V. Grushin, “Asymptotic Behavior of the Eigenvalues of the Schrödinger Operator in Thin Closed Tubes”, Math. Notes, 83:4 (2008), 463–477  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Bikmetov A.R., Gadyl'shin R.R., “On local perturbations of waveguides”, Russ. J. Math. Phys., 23:1 (2016), 1–18  crossref  mathscinet  zmath  isi  scopus
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