Decay estimate of solutions to the sixth order damped Boussinesq equation

摘要

In this paper, we consider the initial value problem for the sixth order damped Boussinesq equation. We prove the global existence and asymptotic behavior of solutions for all space dimensions n⩾1 provided that the initial value is suitably small. Moreover, we show that the solution can be approximated by the linear solution as time tends to infinity for n⩾2. The result slightly improves the result obtained by Wang (2012) [3].