强阻尼波动方程组解的性质  

The Properties of Solution for Strongly Damped Wave Equations

作　　者：李金蔚[1] 蒲志林[1] 邓伟[2] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066 [2]中国民航飞行学院计算机学院,四川广汉618307

出　　处：《四川师范大学学报（自然科学版）》2013年第5期649-654,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10971147)资助项目

摘　　要：运用了Potential Well方法研究了一类强阻尼波动方程组初边值问题在Rn解的存在性,定义了该方程组的位势深度d,运用Poincaré-Soblev嵌入定理证明了位势深度d>0,再通过构建适当的能量函数E(t),稳定集和不稳定集,当初始值属于不稳定集时,解在有限时间爆破和解的衰减估计.The global existence of solution for a class of strongly damped wave equations with initial-boundary value problem is studied by using Potential Well method. The Potential depth of this problem are defined, and by using Poincare-Sobolev embedding theorem, it is proved that the potential depth is a positive number. The concepts of the energy function, the stable and unstable sets are defined, the existence of global solutions under some conditions is proved. It is also proved that if the initial data belong to the unstable set. the solution is blowed up in finite time. the decay behavior of solution is disscussed.

关 键 词：阻尼波动方程 初边值问题 Nehari流形 位势井 稳定集 不稳定集 爆破 衰减估计 

分 类 号：O175.29[理学—数学]