Potential well method for a class of fourth order wave equations with newtonian potential

Abstract

In this paper, we investigate the initial boundary value problem for a fourth order wave equation with Newtonian potential. We establish firstly the local existence of solutions by Banach fixed point theorem. Using the potential well argument, we show the global existence, finite time blow-up, asymptotic behavior of solutions since the initial energy is not over the depth of the potential well. Finally, when the initial energy is supercritical, we give some explicit criterion for blow-up in finite time.