Global existence and blow-up phenomena for a nonlinear wave equation

In this paper, we study the solution to the initial boundary value problem for a class of nonlinear wave equations with damping and source term. By using the energy compensation method, we prove that under some conditions on the initial value, the growth orders of the nonlinear strain term, the damping term, and the source term, the solution to the problem exists globally and blows up respectively, and the estimate for the blow-up time is given.