一阶半线性双曲型方程组的精确边界能控性与能观性  

Exact Boundary Controllability and Exact Boundary Observability for First Order Semilinear Hyperbolic Systems

作　　者：叶莎莎[1] 

机构地区：[1]复旦大学数学科学学院,上海200433

出　　处：《工程数学学报》2007年第5期864-878,共15页Chinese Journal of Engineering Mathematics

摘　　要：本文以一阶半线性双曲型方程组混合初边值问题的整体C^1解理论为基础,采用直接构造的方法建立了一阶半线性双曲组的整体精确边界能控性及能观性理论,对于相应的控制及观测时间给出了精确的估计,并揭示了精确能控性与能观性之间隐含的某种对偶关系。本文还揭示了在非自治系统的情形下,精确能控性与能观性的对偶关系有可能会丧失。By means of a direct method, this paper discusses the global exact controllability and the global exact observability for semilinear hyperbolic systems with general nonlinear boundary conditions. Some sharp estimates on the exact controllability time and the exact observability time are obtained. Moreover, we show that there is an implicit duality between the exact controllability and the exact observability for semilinear hyperbolic systems. However, in the case of nonautonomous systems, this kind of duality may be lost, which reflects the essential difference between the nonautonomous systems and the autonomous systems.

关 键 词：一阶半线性双曲型方程组 精确边界能控性 精确边界能观性 对偶性 

分 类 号：O175.27[理学—数学]