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Asymptotic behavior of a solution of the Cauchy problem for the generalized damped multidimensional Boussinesq equation. (English) Zbl 1452.35157

Summary: This work studies the Cauchy problem for the generalized damped multidimensional Boussinesq equation. By using a multiplier method, it is proven that the global solution of the problem decays to zero exponentially as the time approaches infinity, under a very simple and mild assumption regarding the nonlinear term.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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References:

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