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Waves in a fluid over an elastic bottom. The existence theorem and exact solutions. (English. Russian original) Zbl 0830.35099
Math. Notes 54, No. 6, 1208-1222 (1993); translation from Mat. Zametki 54, No. 6, 33-55 (1993).
We study a linear model that describes waves in a fluid over an elastic bottom. We state a mathematically precise Cauchy problem for this model. We first derive existence and uniqueness theorems, obtaining some a priori estimates for the solution, and then obtain some exact and approximate solutions (quasi-classical asymptotics).
In addition, by the physical formulation of the problem we are interested in the case where the reservoir bottom is uneven, which produces variable coefficients. We also study the Cauchy problem for sufficiently large times.

MSC:
35Q35 PDEs in connection with fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
74B05 Classical linear elasticity
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