On the problem of time-harmonic water waves in the presence of a freely floating structure
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- by N. Kuznetsov
- St. Petersburg Math. J. 22 (2011), 985-995
- DOI: https://doi.org/10.1090/S1061-0022-2011-01179-3
- Published electronically: August 19, 2011
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Abstract:
The two-dimensional problem of time-harmonic water waves in the presence of a freely floating structure (it consists of a finite number of infinitely long surface-piercing cylinders connected above the water surface) is considered. The coupled spectral boundary value problem modeling the small-amplitude motion of this mechanical system involves the spectral parameter, the frequency of oscillations, which appears in the boundary conditions as well as in the equations governing the structure’s motion. It is proved that any value of the frequency turns out to be an eigenvalue of the problem for a particular structure obtained with the help of the so-called inverse procedure.References
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Bibliographic Information
- N. Kuznetsov
- Affiliation: Institute of Mechanical Engineering Problems, Russian Academy of Sciences, Bol′shoĭ Pr. 61, St. Petersburg 199178, Russia
- MR Author ID: 242194
- Email: nikolay.g.kuznetsov@gmail.com
- Received by editor(s): April 5, 2010
- Published electronically: August 19, 2011
- Additional Notes: The author is indebted to Dr. O. Motygin for stimulating discussions and to Professor S. Nazarov for his comments on the first version of the paper
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 985-995
- MSC (2010): Primary 76B15, 76B03; Secondary 35Q35, 35P05
- DOI: https://doi.org/10.1090/S1061-0022-2011-01179-3
- MathSciNet review: 2760090
Dedicated: To V. M. Babich on the occasion of his 80th birthday