充分非线性KdV—Burgers方程的全局边界稳定性

Global boundary stabilization of sufficiently nonlinear Korteweg-de Vries-Burgers equation

讨论了定义于闭区间[0,1]上的充分非线性KdV-Burgers方程在给定边界反馈条件下的稳 定性问题,应用Banach不动点定理和算子半群理论证明了充分非线性KdV-Burgers方程在给定 边界反馈条件下解是存在唯一的;并应用一些不等式和分部积分理论证明了该方程的解在L2意义 下是全局指数稳定的,在H3意义下是全局渐近稳定的,以及在H3意义下是半全局指数稳定的,从 而为该方程的实际应用奠定了理论基础.

Problem of stabilization by boundary feedback conditions for the sufficiently nonlinear Korte-weg-de Vries-Burgers equation on domain [ 0,1 ] is studied. The Banach contraction fixed point theorem and semi group theory are used to prove the uniqueness and existence of the solution of the sufficiently nonlinear Korteweg-de Vries-Burgers equation by boundary feedback conditions. Some usual inequali-ties and integration by parts are used to show that the equation is in L -global exponential stability, H3 -global asymptotic stability, and H3-semi global exponential stability, and is feasible for practical applications.