摘要
讨论了一类非线性四阶波动方程utt+Δ2u+u=up-1u的初边值问题的爆破性质.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 solution for the initial-boundary value problem for a kind of fourth-order wave 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 solution will blow up in finite time when the initial value stays in the unstable set and the positive initial energy is appropriately small.
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2004年第4期545-548,共4页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金资助项目(10301026)
重庆交通学院科研基金资助项目.
关键词
非线性四阶波动方程
初边值问题
不稳定集
凸性分析方法
爆破
nonlinear fourth-order wave equations
initial-boundary value problem
unstable set
convexity method
blow up
