高初始能量下具阻尼项的Klein-Gordon方程解的整体存在性

Global Existence of Solutions for Damped Klein-Gordon Equations with High Initial Energy

采用能量方法和凹性方法研究具阻尼项的Klein-Gordon方程的Cauchy问题.通过构建稳定集并证明其不变性,得到了解的整体存在性.结果表明,高初始能量下具阻尼项的Klein-Gordon方程的解在一定条件下可以整体存在.

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.