由半线性偏微分方程描写的系统的能控性理论

In this project, we have developed a direct meted for the observbility.estimate and obtained its wide applications. We have developed a general method for the exact controllability of semilinear distributed parameter system with Lipschtitz nonlinearities; specially, we obtained the exact controllability of some semilinear evolution equations with nonlinearities growing superlinearly at infinity. We have developed a unified theory, in some sense, for the controllability of the parabolic and.hyperbolc systems. We derived the global unique continuation property for some.partial differential equations with nonsmooth coefficients. We found a new sigular phenomenon that the global unique continuation property of a class of partial differential equations depends very strongly on the zero set of the coefficients of its lower order terms even if these coefficients are in the class of analytic functions. Also, we obtain several results on the long time behavior of partial differential equations, on.stabilization with indefinte damping, on inverse problems and so on. Our works.attracted the interest of domestic and international colleagues.

该项目主要研究由物理学提出的半线性偏微分方程，如半线性的波方程、板方程、薛定谔方程及弹性力学方程组等所描写的系统的能控性，以及某些与之相关的问题如系统的能观性，能稳性和最优控制理论等。这些问题皆是目前国际上该领域研究的特点，且有相当于的难度。另一方面，这项研究对具体的工程技术实践有指导作用。