一类带漂移-扩散项的非线性抛物型方程组的能控性  

Controllability of a Nonlinear Parabolic Systems with Drift-Diffusion Term

作　　者：张志朋 张亮 Zhang Zhipeng;Zhang Liang(Department of Mathematics,Wuhan University of Technology,Wuhan 430070)

机构地区：[1]武汉理工大学理学院数学系,武汉430070

出　　处：《数学物理学报（A辑）》2023年第6期1744-1758,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(61573012)。

摘　　要：该文研究一类非线性抛物型方程组的能控性问题及其时间最优控制的存在性问题.该方程具有漂移-扩散项和非线性项h(u,v),g(u,v).文中利用半群的L^(p)-L^(q)估计和近年来发展的最大正则化研究方程组的正则性和控制函数的估计,利用不动点定理证明了非线性系统的局部精确能控性,并将该结论应用于证明时间最优控制的存在性.This paper studies the controllability and the existence of time optimal control for a class of nonlinear parabolic equations,which has drift-diffusion term with nonlinear terms h(u,v) and g(u,v).It applies the L^(p)-L^(q) estimate of semigroups and the recently developed maximal regularity theory to study the regularity and the cost estimate of control functions.Moreover,this paper establishes the local exact controllability of the nonlinear control system by utilizing the Kakutani's fixed point theorem.Therefore,it is applied to the existence of time optimal controls.

关 键 词：抛物型方程组 能观性估计 精确能控性 Kakutani不动点 

分 类 号：O231.4[理学—运筹学与控制论]