Global existence and asymptotic behavior of solution for the sixth order Boussinesq equation with damped term

We investigate the small-data Cauchy problem for the sixth order Boussinesq equation with damped term. The decay estimates of solutions to the corresponding linear equation are given by using the dyadic decomposition and some properties of Bessel functions. Then, we prove the global existence and asymptotic of the small amplitude solution in the time-weighted Sobolev space by the contraction mapping principle.