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Global existence and asymptotic behaviour of solutions for the generalized Boussinesq equation. (English) Zbl 1161.35470
Summary: We prove the existence and the uniqueness of global solution for the Cauchy problem for the generalized Boussinesq equation. Under some assumptions, we also show that the $L_\infty$ norm of small solution of the Cauchy problem for the generalized Boussinesq equation decays to zero as $t$ tends to infinity.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 35B45 A priori estimates for solutions of PDE 35B40 Asymptotic behavior of solutions of PDE 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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##### References:
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