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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 5, Pages 1086–1101 (Mi smj2148)  
This article is cited in 66 scientific papers (total in 66 papers)

Variational and asymptotic methods for finding eigenvalues below the continuous spectrum threshold

S. A. Nazarov

Institute of Problems of Mechanical Engineering, St. Petersburg, Russia
Full-text PDF (388 kB) Citations (66)
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Abstract: Considering the example of a mixed boundary value problem for the Helmholtz operator we discuss two methods for finding eigenvalues below the continuous spectrum threshold: one variational and the other – asymptotic. We construct asymptotics for the eigenvalue arising near the threshold as a small obstacle appears in the cylindrical waveguide. The resulting asymptotic formula, its derivation and justification differ substantially from the case of a bounded domain.
Keywords: eigenvalue, discrete spectrum, waveguide, Helmholtz equation, trapped mode.
Received: 20.08.2009
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 5, Pages 866–878
DOI: https://doi.org/10.1007/s11202-010-0087-3
Bibliographic databases:
Document Type: Article
UDC: 519.968:535.4:531.33
Language: Russian
Citation: S. A. Nazarov, “Variational and asymptotic methods for finding eigenvalues below the continuous spectrum threshold”, Sibirsk. Mat. Zh., 51:5 (2010), 1086–1101; Siberian Math. J., 51:5 (2010), 866–878
Citation in format AMSBIB
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    • This publication is cited in the following 66 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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    References:89
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