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An operator model for the oscillation problem of liquids on an elastic bottom. (English. Russian original) Zbl 0973.35140
Math. Notes 68, No. 1, 57-70 (2000); translation from Mat. Zametki 68, No. 1, 66-81 (2000).
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 and explained. The main aim of this paper is to recast these equations in the form \[ A\ddot \omega(t) + T\omega(t) = 0, \] where \(A\) and \(T\) are positive operators in the function space naturally corresponding to the problem.

35L90 Abstract hyperbolic equations
76E99 Hydrodynamic stability