K-S方程边界控制的全局指数稳定估计

Global Exponential Stability Estimate of K-S Equation by Boundary Control

边界控制是分布参数控制系统的受控形式之一 笔者在区间[0,1]上利用边界控制来研究K S方程的全局指数稳定性问题 首先通过Banach不动点定理和算子半群理论证明解的存在性和唯一性,然后证明K S方程在笔者所给定的边界反馈条件下是L2全局指数稳定的

Boundary control is one of the control forms of the distribute parameter controlled system. The problem of global exponential stabilitization by boundary control for the KS equation on the domain is considered. The global existence and uniqueness of the solutions with the help of the Banach fixed point theorem and the theory of operator semigroups are verified. The global exponential stability of KS equation with the boudary feedbacks given by authors is also proved. It shows that decay rate estimates depend not only on the diffusion coefficient but also on the dispersion coefficient.