具有两个异号非线性源项波动方程解的爆破  

Blow up of solutions for wave equations with two nonlinear source terms of different signs

作　　者：罗显康[1] 崔泽健[2] 

机构地区：[1]宜宾学院数学与应用数学系,宜宾644000 [2]西华师范大学数学与信息学院,南充637002

出　　处：《四川大学学报（自然科学版）》2011年第3期495-498,共4页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(10225102);宜宾学院青年基金(2008QJ24)

摘　　要：作者讨论了具有两个异号非线性源项波动方程u_a-△u+a|u|^(p-1)u-b|u|^(q-1)u=0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,作者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 wave equations with two nonlinear source terms of different signs 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：半线性波动方程 势井 不稳定集 凸性分析方法 爆破 

分 类 号：O175.26[理学—数学]