移动边界区域上变系数波方程的能控性与镇定性研究

Controllability and stabilization of wave equations is an important problem of control theory of distributed parameter systems, wave equation model with variable coefficients is closer to actual physical process. Many of the actual physical process are performed in domains with moving boundary. By means of the inherent nonlinear framework of differential geometry, controllability of wave equations with variable coefficients has become an important research direction. The project is concerned with controllability and stabilization of wave equations with variable coefficients in domains with moving boundary. The main tool is the Riemannian geometry method: by combining the Riemannian geometry method with the classic methods of control theory, and overcoming the difficulties of variable coefficients and moving boundary, under some appropriate geometric conditions and domain conditions, the exact controllability and stabilization results are established for the problem in domains with moving boundary, necessary theoretical basis are provided for the control of the corresponding physical processes.

波动方程的能控性与镇定问题是分布参数系统控制理论的重要问题，变系数波方程是更接近实际物理过程的模型，许多实际的物理过程则是在边界随时间移动的区域中进行的。借助微分几何的固有非线性框架来研究变系数波方程的能控性，已经成为目前重要的研究方向之一。本项目研究一类变系数波方程系统在具有移动边界区域上的能控性与镇定问题。主要应用黎曼几何方法：将黎曼几何方法与分布参数系统控制理论中的经典方法相结合，克服变系数与移动边界产生的困难，在适当的几何条件和区域条件下，得到变系数波方程的边界精确能控和镇定性结论，为相应的物理过程的控制提供必要的理论依据。

变系数波方程系统的能控性与镇定问题是分布参数系统控制理论的重要问题，许多实际的物理过程则是在边界随时间移动的区域中进行的。本项目主要研究变系数波方程系统在具有移动边界区域上的能控性与镇定问题。在适当的系数条件和区域条件下，得到了变系数波方程系统的边界精确能控和镇定性结论。