关键词: Klein-Gordon方程, 高初始能量, 整体存在性, 稳定集, 凹性方法

Abstract:

We studied the Cauchy problem of damped Klein-Gordon equations  using the energy method and the concavity method. The global existence of solutions was obtained by constructing a stable set and proving its invariance. The results  show that the solutions of damped Klein-Gordon equations with high initial energy may also exist globally under certain conditions.

Key words: KleinGordon equation, high initial energy, global existence, stable set, concavity method