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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm7798https://doi.org/10.1070/SM2012v203n02ABEH004217 https://www.mathnet.ru/eng/sm/v203/i2/p3
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Abstract page: | 1238 | Russian version PDF: | 227 | English version PDF: | 19 | References: | 103 | First page: | 33 |
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