具有全局Lipschitz非线性条件的抛物系统的精确能控性  

Exact Controllability of Systems Governed by Parabolic Differential Equations with Globally Lipschitz Nonlinearities

作　　者：颜于清[1] 赵怡[1] 

机构地区：[1]中山大学数学与计算科学学院,广东广州510275

出　　处：《中山大学学报（自然科学版）》2007年第3期10-13,共4页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10371136)

摘　　要：考察了带有满足全局Lipschitz条件的非线性项的抛物系统在有界状态域上的精确能控制性问题。当目标状态限制于H2(Ω)时,证明了该抛物非线性系统是精确能控的。证明过程主要运用了Schauder不动点方法。The semilinear heat equation involving globally Lipschitz nonlinearities in a bounded domain of Rn is studied. The system is proved to be exact controllable when the terminal state belongs to the Sobolev space of functions having two square integrable derivatives. The proof uses a variant of a classical Schauder＇s fixed point method.

关 键 词：精确能控性 全局Lipschitz Schauder不动点方法 

分 类 号：O231.2[理学—运筹学与控制论]