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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 397, Pages 89–114 (Mi znsl4669)  

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

Double-sided estimates for eigenfrequencies in the John problem for freely floating body

S. A. Nazarova, J. Taskinenb

a Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
b University of Helsinki, Department of Mathematics and Statistics, Helsinki, Finland
Full-text PDF (333 kB) Citations (1)
References:
Abstract: The two-dimensional problem on oblique incident waves and a freely floating cylinder is reduced to the study of the spectrum of a suitable self-adjoint operator in Hilbert space. Using tools from spectral measure theory we estimate the difference between eigenfrequencies of the original problem and a problem on an inert body, which does not react to the buoyancy forces. We give the localization of eigenfrequencies of the freely floating body, and in addition derive a sufficient condition for the existence of the point spectrum in the corresponding boundary value problem.
Key words and phrases: surface waves, trapped modes, freely floating body, comparison principle.
Received: 18.10.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 185, Issue 5, Pages 707–720
DOI: https://doi.org/10.1007/s10958-012-0954-5
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: S. A. Nazarov, J. Taskinen, “Double-sided estimates for eigenfrequencies in the John problem for freely floating body”, Boundary-value problems of mathematical physics and related problems of function theory. Part 42, Zap. Nauchn. Sem. POMI, 397, POMI, St. Petersburg, 2011, 89–114; J. Math. Sci. (N. Y.), 185:5 (2012), 707–720
Citation in format AMSBIB
\Bibitem{NazTas11}
\by S.~A.~Nazarov, J.~Taskinen
\paper Double-sided estimates for eigenfrequencies in the John problem for freely floating body
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~42
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 397
\pages 89--114
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4669}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2870110}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 185
\issue 5
\pages 707--720
\crossref{https://doi.org/10.1007/s10958-012-0954-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866927088}
Linking options:
  • https://www.mathnet.ru/eng/znsl4669
  • https://www.mathnet.ru/eng/znsl/v397/p89
  • This publication is cited in the following 1 articles:
    1. Nazarov S.A. Ruotsalainen K.M., “Criteria For Trapped Modes in a Cranked Channel With Fixed and Freely Floating Bodies”, Z. Angew. Math. Phys., 65:5 (2014), 977–1002  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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