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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 348, Pages 98–126 (Mi znsl63)  

This article is cited in 10 scientific papers (total in 10 papers)

On the concentration of the point spectrum on the continuous one in problems of the linearized theory of water-waves

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
References:
Abstract: For the linearized theory of water-waves, we find out families of submersed or surface-piercing bodies in an infinite three-dimensional channel which depend on the small parameter $\varepsilon>0$ and have the following property: For any positive $d$ and integer $J$, there exists $\varepsilon(d,J)>0$ such that, for $\varepsilon\in(0,\varepsilon(d,J)]$, the segment $[0,d]$ of the continuous spectrum of the problem contains at least $J$ eigenvalues. These eigenvalues are associated with trapped modes, i.e., solutions of the homogeneous problem which decay exponentially at infinity and possess a finite energy.
Received: 05.11.2007
English version:
Journal of Mathematical Sciences (New York), 2008, Volume 152, Issue 5, Pages 674–689
DOI: https://doi.org/10.1007/s10958-008-9095-2
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: S. A. Nazarov, “On the concentration of the point spectrum on the continuous one in problems of the linearized theory of water-waves”, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Zap. Nauchn. Sem. POMI, 348, POMI, St. Petersburg, 2007, 98–126; J. Math. Sci. (N. Y.), 152:5 (2008), 674–689
Citation in format AMSBIB
\Bibitem{Naz07}
\by S.~A.~Nazarov
\paper On the concentration of the point spectrum on the
continuous one in problems of the linearized theory of water-waves
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~38
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 348
\pages 98--126
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl63}
\elib{https://elibrary.ru/item.asp?id=13077194}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 152
\issue 5
\pages 674--689
\crossref{https://doi.org/10.1007/s10958-008-9095-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-51749110661}
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  • https://www.mathnet.ru/eng/znsl63
  • https://www.mathnet.ru/eng/znsl/v348/p98
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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