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Zap. Nauchn. Sem. POMI, 2011, Volume 393, Pages 46–79 (Mi znsl4615)  

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotics of frequency of a surface wave trapped by a slightly inclined barrier in a liquid layer

J. H. Videmana, V. Chiado' Piatb, S. A. Nazarovc

a CEMAT/Departamento de Matematica, Instituto Superior Tecnico, Lisboa, Portugal
b Politcnico of Torino, Torino, Italy
c Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We consider the two-dimensional formulation of the problem on an oblique surface wave for an obstacle in the shape of a submerged strip-barrier. If the barrier is vertical, the discrete spectrum of the problem is empty, but for an inclined barrier there appear an eigenvalue below the threshold of the continuous spectrum and the corresponding trapped mode which decays exponentially in the direction, perpendicular to the obstacle. The asymptotics of the eigenvalue is found in the case of a small inclination angle.

Key words and phrases: trapped mode, water-wave, discrete spectrum, asymptotic behaviour of eigenvalues.

Full text: PDF file (411 kB)
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English version:
Journal of Mathematical Sciences (New York), 2012, 185:4, 536–553

Bibliographic databases:

UDC: 517.958+531.327.13+517.956.8
Received: 05.09.2011

Citation: J. H. Videman, V. Chiado' Piat, S. A. Nazarov, “Asymptotics of frequency of a surface wave trapped by a slightly inclined barrier in a liquid layer”, Mathematical problems in the theory of wave propagation. Part 41, Zap. Nauchn. Sem. POMI, 393, POMI, St. Petersburg, 2011, 46–79; J. Math. Sci. (N. Y.), 185:4 (2012), 536–553

Citation in format AMSBIB
\Bibitem{VidChiNaz11}
\by J.~H.~Videman, V.~Chiado' Piat, S.~A.~Nazarov
\paper Asymptotics of frequency of a~surface wave trapped by a~slightly inclined barrier in a~liquid layer
\inbook Mathematical problems in the theory of wave propagation. Part~41
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 393
\pages 46--79
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4615}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2870204}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 185
\issue 4
\pages 536--553
\crossref{https://doi.org/10.1007/s10958-012-0937-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866541109}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Piat V.Ch. Nazarov S.A. Taskinen J., “Embedded Eigenvalues Forwater-Waves in Athree-Dimensional Channel With Athin Screen”, Q. J. Mech. Appl. Math., 71:2 (2018), 187–220  crossref  mathscinet  isi  scopus
  • Записки научных семинаров ПОМИ
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