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The long-time behavior of solutions of a nonlinear fourth-order wave equation, describing the dynamics of marine risers. (English) Zbl 0881.76015

Summary: The fourth-order nonlinear equation describing the dynamics of marine risers is considered. It is established that the zero solution of the boundary value problem for the considered equation is globally asymptotically stable. Moreover, an estimate of the decay rate of the solutions is obtained.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76E20 Stability and instability of geophysical and astrophysical flows
86A05 Hydrology, hydrography, oceanography
35Q35 PDEs in connection with fluid mechanics
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References:

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[5] : Variational methods in mathematics, science and engineering. D. Reidel Publishing company, Dordrecht–Boston–London 1975.
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