A sufficient condition for finite time blow up of the nonlinear Klein-Gordon equations with arbitrarily positive initial energy

Details A sufficient condition for finite time blow up of the nonlinear Klein-Gordon equations with arbitrarily positive initial energy A sufficient condition for finite time blow up of the nonlinear Klein-Gordon equations with arbitrarily positive initial energy

2007-02-07

arxiv.org/abs/math/0702187v1

Mathematics

Analysis of PDEs

6pages

Scientific paper

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.

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