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Matematicheskie Zametki, 1997, Volume 61, Issue 4, Pages 494–502
DOI: https://doi.org/10.4213/mzm1529 (Mi mzm1529) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Characteristic frequencies of bodies with thin spikes. III. Frequency splitting

R. R. Gadyl'shin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Full-text PDF (188 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm1529
Abstract: The eigenvalue problem for the Laplace operator with the Neumann boundary conditions in a domain that has a thin spike of finite length is considered for the case in which the limit value is an eigenvalue both for the main body and the spike. The method of matched asymptotic expansions is used to construct total asymptotics of the eigenvalues of the perturbed problem and obtain closed formulas for the leading asymptotic terms.
Received: 22.12.1994
English version:
Mathematical Notes, 1997, Volume 61, Issue 4, Pages 409–416
DOI: https://doi.org/10.1007/BF02354985
Bibliographic databases:
UDC: 517
Language: Russian
Citation: R. R. Gadyl'shin, “Characteristic frequencies of bodies with thin spikes. III. Frequency splitting”, Mat. Zametki, 61:4 (1997), 494–502; Math. Notes, 61:4 (1997), 409–416
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm1529
  • https://doi.org/10.4213/mzm1529
  • https://www.mathnet.ru/eng/mzm/v61/i4/p494
    Cycle of papers
    This publication is cited in the following 5 articles:
    1. D. I. Borisov, “Norm Resolvent Convergence of Elliptic Operators in Domains with Thin Spikes”, J Math Sci, 261:3 (2022), 366  crossref
    2. Bucur D. Henrot A. Michetti M., “Asymptotic Behaviour of the Steklov Spectrum on Dumbbell Domains”, Commun. Partial Differ. Equ., 46:2 (2021), 362–393  crossref  isi
    3. Nazarov S.A., “Anomalies of Acoustic Wave Scattering Near the Cut-Off Points of Continuous Spectrum (a Review)”, Acoust. Phys., 66:5 (2020), 477–494  crossref  isi
    4. R. R. Gadyl'shin, “On the eigenvalues of a “dumb-bell with a thin handle””, Izv. Math., 69:2 (2005), 265–329  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Gadyl'shin, RR, “Eigenvalues of the Neumann problem in a domain with a thin channel”, Doklady Mathematics, 66:3 (2002), 436  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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