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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 348, Pages 98–126
(Mi znsl63)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/znsl63 https://www.mathnet.ru/eng/znsl/v348/p98
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Abstract page: | 438 | Full-text PDF : | 101 | References: | 85 |
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