Global existence and asymptotic behaviour of solutions for the generalized Boussinesq equation

In this paper, 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∞L∞ norm of small solution of the Cauchy problem for the generalized Boussinesq equation decays to zero as tt tends to the infinity.