Aceive耗散色散方程边界控制全局指数稳定估计

Global Exponential Stability Estimate of Aceive Diffusion and Dispersion Equation by Boundary Control

在区间[0,1]上利用边界控制来研究Aceive耗散色散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,应用一些不等式和分部积分理论证明Aceive耗散色散方程在边界控制律u(0,t)=ux(0,t)=u(1,t)=0,uxx(1,t)=-α2ux(1,t)下是L2全局指数稳定的.

The problem of exponential stabilization by boundary control for the Aceive diffusion and dispersion equation on the domain [ 0,1 ] is considered. The global existence and uniqueness of the solutions with the help of the Banach Fixed point theory and the theory of operator semi - group are verified. Using some usual inequalities and intergration by parts, we derive a control law of the u （0, t）= ux （0, t） = u （ 1 , t） = 0, uxx （ 1, t） = -α/2-ux（1, t）,a and prove that it guarantees L2 - global exponential stability.