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Sbornik: Mathematics, 2012, Volume 203, Issue 2, Pages 153–182
DOI: https://doi.org/10.1070/SM2012v203n02ABEH004217
(Mi sm7798)
 

This article is cited in 24 scientific papers (total in 24 papers)

Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide

G. Cardonea, S. A. Nazarovb, K. Ruotsalainenc

a Facoltà di Ingegneria, Università degli Studi del Sannio
b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg
c University of Oulu
References:
Abstract: The existence of an eigenvalue embedded in the continuous spectrum is proved for the Neumann problem for Helmholtz's equation in a two-dimensional waveguide with two outlets to infinity which are half-strips of width $1$ and $1-\varepsilon$, where $\varepsilon>0$ is a small parameter. The width function of the part of the waveguide connecting these outlets is of order $\sqrt{\varepsilon}$; it is defined as a linear combination of three fairly arbitrary functions, whose coefficients are obtained from a certain nonlinear equation. The result is derived from an asymptotic analysis of an auxiliary object, the augmented scattering matrix.
Bibliography: 29 titles.
Keywords: acoustic waveguide, water waves in a channel, eigenvalues in the continuous spectrum, asymptotic behaviour, augmented scattering matrix.
Received: 11.10.2010 and 28.04.2011
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 2, Pages 3–32
DOI: https://doi.org/10.4213/sm7798
Bibliographic databases:
Document Type: Article
UDC: 517.956.8+517.956.227
MSC: Primary 35J05, 35P05; Secondary 35P25
Language: English
Original paper language: Russian
Citation: G. Cardone, S. A. Nazarov, K. Ruotsalainen, “Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide”, Mat. Sb., 203:2 (2012), 3–32; Sb. Math., 203:2 (2012), 153–182
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2012v203n02ABEH004217
  • https://www.mathnet.ru/eng/sm/v203/i2/p3
  • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математический сборник Sbornik: Mathematics
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    Abstract page:1240
    Russian version PDF:230
    English version PDF:20
    References:104
    First page:33
     
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