一类非线性Klein-Gordon方程初边值问题解的爆破  

Blow up of solutions of initial boundary value problem for a class of nonlinear Klein-Gordon equations

作　　者：罗显康[1] 

机构地区：[1]宜宾学院数学与应用数学系,四川宜宾644007

出　　处：《西南民族大学学报（自然科学版）》2010年第1期21-24,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10301026;10225102);宜宾学院青年基金

摘　　要：讨论了一类非线性Klein-Gordon方程utt-Δu+u=︱u︱p-1u的初边值问题解的爆破性质.依据势井理论,通过构造不稳定集,结合凸性分析方法证明了:初值属于不稳定集,初始能量为正但有适当上界时解将发生爆破.Blow-up property of the solutions for a class of nonlinear Klein-Gordon equations is considered. According to the potential well theory, the unstable set is constructed. By using the property of the unstable set and the convexity method, it is proved that the solutions will blow-up in finite time when the initial value stays in the unstable set and the positive initial energy is appropriately small.

关 键 词：KLEIN-GORDON方程 势井 不稳定集 凸性分析方法 爆破 

分 类 号：O175.29[理学—数学]