Classification of Blow-up and Global Existence of Solutions to a System of Petrovsky Equations

Abstract

In this paper, we investigate global existence, uniform decay, and blow-up of solutions for a class of system of Petrovsky equations containing nonlinear damping and sources. By introducing a family of potential wells, we not only obtain the invariant sets and vacuum isolating of solutions but also give some threshold results of global existence and nonexistence of solutions. Furthermore, by using energy techniques, we also establish certain qualitative estimates for solution.