caa a22 4500 475740181 CHVBK 20180406123457.0 cr unu---uuuuu 170329e20000701xx s 000 0 eng 10.1007/BF02674646 doi (NATIONALLICENCE)springer-10.1007/BF02674646 An operator model for the oscillation problem of liquids on an elastic bottom [Elektronische Daten] [R. Griniv, S. Dobrokhotov, A. Shkalikov] 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 1 $$\mathcal{A}\ddot w(t) + \mathcal{T}w(t) = 0,$$ , where $$\mathcal{A}$$ and $$\mathcal{T}$$ are positive operators in the function space naturally corresponding to the problem. The further aim is to investigate the spectrum of the linear pencil $$\lambda \mathcal{A}\dag \mathcal{T}$$ , which determines the dynamics of the problem. Kluwer Academic/Plenum Publishers, 2000 operator models in hydrodynamics nationallicence linear operator pencils nationallicence spectral problems nationallicence small oscillations nationallicence surface waves nationallicence elastic bottom nationallicence Euler-Lagrange equations nationallicence Griniv R. Institute for Applied Problems of Mechanics and Mathematics, National Ukranien Academy of Science, Lviv aut Dobrokhotov S. Institute for Problems of Mechanics of Russian Academy of Science, Moscow aut Shkalikov A. M. V. Lomonosov Moscow State University, Moscow aut Mathematical Notes Springer Netherlands 68/1(2000-07-01), 57-70 0001-4346 68:1<57 2000 68 11006 https://doi.org/10.1007/BF02674646 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02674646 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Griniv R. Institute for Applied Problems of Mechanics and Mathematics, National Ukranien Academy of Science, Lviv aut NATIONALLICENCE 700 1- Dobrokhotov S. Institute for Problems of Mechanics of Russian Academy of Science, Moscow aut NATIONALLICENCE 700 1- Shkalikov A. M. V. Lomonosov Moscow State University, Moscow aut NATIONALLICENCE 773 0- Mathematical Notes Springer Netherlands 68/1(2000-07-01), 57-70 0001-4346 68:1<57 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer