Ying Wang University of Electronic Science and Technology of China
Abstract : In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.
Keywords : Cauchy problem, sixth-order wave equation, blow-up, existence of global solution