In this paper, we discuss the nonlinear wave equations with nonlinear damping and source terms. By using the potential well methods, we get a result for the global existence and blow-up of the solutions.
We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.
Global existence and blow-up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations