In this paper we consider the nonexistence of global solutions of a Klein-Gordon equation of the form \begin{ eqnarray*} u_{ tt}-\Delta u+m^2u=f(u)& (t,x)\in [0,T)\times\R^n. \end{ eqnarray*} Here $m\neq 0$ and the nonlinear power $f(u)$ satisfies some assumptions which will be stated later. We give a sufficient condition on the initial datum with arbitrarily high initial energy such that the solution of the above Klein-Gordon equation blows up in a finite time.
Categories: math.AP
