An operator model for the oscillation problem of liquids on an elastic bottom |
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| Authors: | R O Griniv S Yu Dobrokhotov A A Shkalikov |
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| Institution: | (1) Institute for Applied Problems of Mechanics and Mathematics, National Ukranien Academy of Science, Lviv;(2) Institute for Problems of Mechanics of Russian Academy of Science, Moscow;(3) M. V. Lomonosov Moscow State University, Moscow |
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| Abstract: | This paper deals with the problem of small oscillations in a liquid layer of finite depth under the assumption that the bottom
is an elastic medium. The system of equations corresponding to the problem is written out and explained. The main aim of the
paper is to recast these equations in the form
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(1) |
, where
and
are positive operators in the function space naturally corresponding to the problem. The further aim is to investigate the
spectrum of the linear pencil
, which determines the dynamics of the problem.
Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 66–81, July, 2000. |
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| Keywords: | operator models in hydrodynamics linear operator pencils spectral problems small oscillations surface waves elastic bottom Euler-Lagrange equations |
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