一类受控于bang-bang控制的退化抛物系统的近似能控性  

Approximate controllability of a class of coupled degenerate parabolic equations with bang-bang controls

作　　者：杜润梅 刘亚新 DU Run-mei;LIU Ya-xin(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012

出　　处：《吉林师范大学学报（自然科学版）》2021年第2期45-51,共7页Journal of Jilin Normal University:Natural Science Edition

基　　金：吉林省教育厅“十三五”科学技术项目(JJK120200643KJ,JJKH20200679KJ)

摘　　要：选取作用在区域内部的bang-bang控制作为控制函数,利用共轭系统的唯一延拓性证明了一类在边界退化的抛物系统的近似能控性.结果表明,对任意的目标函数均存在一个控制函数,使该问题的解在有限时间内可充分接近目标函数.In the condition of selecting the bang-bang control which acted on the inside of the region as the control function,the approximate controllability of a class of parabolic systems that degenerate at the boundary was proved by using the unique continuation of the conjugate system.The result shows that for any objective function,there exists a control function such that the solution of the problem can fully close to the objective function in a finite time.

关 键 词：退化抛物方程组 近似能控性 耦合方程组 BANG-BANG控制 

分 类 号：O175.26[理学—数学]