Global existence and blowup of solutions for a class of nonlinear higher-order wave equations

In this paper, we consider a class of nonlinear higher-order wave equation with nonlinear damping $$u_{tt}+(-\Delta)^mu+a|u_t|^{p-2}u_t=b|u|^{q-2}u$$ in a bounded domain ${\Omega\subset\mathbb{R}^N}$ (N????1 is a natural number). We show that the solution is global in time under some conditions without the relation between p and q and we also show that the local solution blows up in finite time if q?>?p with some assumptions on initial energy. The decay estimate of the energy function for the global solution and the lifespan for the blow-up solution are given. This extend the recent results of Ye (J Ineq Appl, 2010).