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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 397, Pages 89–114
(Mi znsl4669)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/znsl4669 https://www.mathnet.ru/eng/znsl/v397/p89
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