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.
In this paper, we consider the initial boundary value problem for the p-Laplacian equation with weak and p-Laplacian damping terms, nonlinear boundary, delay and source terms acting on the boundary. By introducing suitable energy and perturbed Lyapunov functionals, we prove global existence, finite time blow up and asymptotic behavior of solutions in cases p > 2 and p = 2. To our best knowledge, there is no results of the p-Laplacian equation with a nonlinear boundary delay term.
Global existence, asymptotic behavior and blow-up of solutions for a suspension bridge equation with nonlinear damping and source terms