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

作者：Wang Yanjin^*

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136(10): 3477-3482.

DOI：10.1090/S0002-9939-08-09514-2

• Klein-Gordon equation
• blow up
• positive initial energy

In this paper we consider the nonexistence of global solutions of a Klein-Gordon equation of the form
u(tt) - Delta u + m(2)u = f( u), (t, x) is an element of[0, T) x R-n.
Here m not equal 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 infinite time.

• 出版日期2008
• 单位北京应用物理与计算数学研究所