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
, 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.
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Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 66–81, July, 2000.
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Griniv, R.O., Dobrokhotov, S.Y. & Shkalikov, A.A. An operator model for the oscillation problem of liquids on an elastic bottom. Math Notes 68, 57–70 (2000). https://doi.org/10.1007/BF02674646
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DOI: https://doi.org/10.1007/BF02674646