Finite time blowup for nonlinear Klein–Gordon equations with arbitrarily positive initial energy

Abstract

This paper is concerned with the finite time blow up of the solution to the Cauchy problem for the Klein–Gordon equation at arbitrarily positive initial energy level. By introducing a new auxiliary function and an adapted concavity method we establish some sufficient conditions on initial data such that the solution blows up in finite time, which extends the results established in Wang (2008).