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The existence of a periodic solution in a tide dynamics problem

Abstract

We examine a quasilinear boundary-value problem describing the dynamics of tidal flow in the sea. For small values of ground friction coefficient and under the fulfillment of a certain condition on the function giving the depth of the sea, we prove the existence of a generalized periodic solution. We construct a difference scheme for the numerical solution of the problem being examined and we prove its stability.

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Literature cited

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    B. A. Kagan, Hydrodynamic Models of Tidal Motions in the Sea [in Russian], Gidrometeoizdat, Leningrad (1968).

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    G. I. Marchuk, R. G. Gordeev, B. A. Kagan, and V. Ya. Rivkind, Numerical Method for the Integration of Tide Dynamics Equations [in Russian], Nauka, Novosibirsk (1972).

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    I. G. Malkin, Certain Problems in the Theory of Nonlinear Oscillations [in Russian], GITTL, Moscow (1956).

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    O. A. Ladyzhenskaya, Mathematical Aspects of the Dynamics of a Viscous Incompressible Liquid [in Russian], Nauka (1970).

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    O. A. Ladyzhenskaya and V. Ya. Rivkind, Izv. Akad. Nauk SSSR, Ser. Matem.,35, No. 2, 3–10 (1971).

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Additional information

Translated from Problemy Matematicheskogo Analiza. No. 4: Integralnye i Differentsial'nye Operatory. Differentsial'nye Uraveniya, pp. 3–9, 1973.

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Gordeev, R.G. The existence of a periodic solution in a tide dynamics problem. J Math Sci 6, 1–4 (1976). https://doi.org/10.1007/BF01084856

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Keywords

  • Friction Coefficient
  • Periodic Solution
  • Difference Scheme
  • Dynamic Problem
  • Tidal Flow