Global existence and finite time blow up for a class of semilinear wave equations on RNRN

In this paper, we consider the initial value problem for a class of semilinear wave equations with damping and source terms. Under certain conditions we establish the global existence of solutions, and the asymptotic behavior of the solutions by introducing an appropriate Lyapunov functions. Moreover, we examine the blow-up in finite time when the initial data is sufficiently large.