一类具有非局部项的抛物方程在Sobolev空间的能控性  

CONTROLLABILITY OF A CLASS OF PARABOLIC EQUATIONS WITH NON-LOCAL TERMS IN SOBOLEV SPACE

作　　者：曾曦 莫玉玲 邓紫娟 刘洁 周秀香 ZENG Xi;MO Yu-ling;DENG Zi-juan;LIU Jie;ZHOU Xiu-xiang(School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang 524048,China)

机构地区：[1]岭南师范学院数学与统计学院

出　　处：《数学杂志》2019年第6期889-898,共10页Journal of Mathematics

基　　金：国家自然科学基金项目资助(11601213);岭南师范学院校级人才引进专项资助(ZL1612);岭南师范学院重点学科项目(1171518004);大学生创新创业训练计划省级立项项目(201910579806)

摘　　要：本文研究了具有非局部项的抛物型偏微分方程在H^m空间的能控性问题.利用构造法和对偶理论,获得了在一定的条件下任意给定一个正整数m,可找到H^m空间中的一类初值使得具有非局部项的抛物型方程不零能控的结果.推广了具有非局部项的抛物型方程在L^2空间不零能控的结果.In this paper, we study the controllability problem for a class of parabolic partial differential equations with non-local terms in H^m space. By construction method and duality theory, we conclude that if an integer m is given, a class of the initial value in the H^m space can be found that the controlled system can not be null controllable under certain conditions, which generalize the result of non controllability problem in the space L^2(0, 1)..

关 键 词：抛物型方程 非局部项 H^m空间 近似能控性 

分 类 号：O231.4[理学—运筹学与控制论]