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Mat. Zametki, 2004, Volume 75, Issue 2, Pages 236–252 (Mi mz30)  

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

Asymptotics of the Eigenelements of the Laplace Operator when the Boundary-Condition Type Changes on a Narrow Flattened Strip

M. Yu. Planida

Bashkir State Pedagogical University

Abstract: In this paper, the method of matching asymptotic expansions is used to construct an asymptotics (in a small parameter) of the eigenvalues and eigenfunctions of the Laplace operator in a domain when the boundary-condition type changes on a narrow flattened strip, provided that on the narrow strip of the boundary a Neumann condition is given and on the remaining part of the boundary a Dirichlet condition is given. The width of the strip is taken as the small parameter.

DOI: https://doi.org/10.4213/mzm30

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English version:
Mathematical Notes, 2004, 75:2, 213–228

Bibliographic databases:

UDC: 517.956
Received: 25.10.2002

Citation: M. Yu. Planida, “Asymptotics of the Eigenelements of the Laplace Operator when the Boundary-Condition Type Changes on a Narrow Flattened Strip”, Mat. Zametki, 75:2 (2004), 236–252; Math. Notes, 75:2 (2004), 213–228

Citation in format AMSBIB
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\transl
\jour Math. Notes
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\pages 213--228
\crossref{https://doi.org/10.1023/B:MATN.0000015037.16768.60}
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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. M. Yu. Planida, “Asymptotics of the eigenelements of the Laplacian with singular perturbations of boundary conditions on narrow and thin sets”, Sb. Math., 196:5 (2005), 703–741  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. R. R. Gadyl'shin, E. A. Shishkina, “On Friedrichs inequalities for a disk”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 44–58  mathnet  crossref  isi  elib
  • Математические заметки Mathematical Notes
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