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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 norm of small solution of the Cauchy problem for the generalized Boussinesq equation decays to zero as t tends to infinity.
MSC:
35Q35PDEs in connection with fluid mechanics
35B45A priori estimates for solutions of PDE
35B40Asymptotic behavior of solutions of PDE
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction