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| 摘要: |
| 本文研究了具有非局部项的抛物型偏微分方程在Hm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Hm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L2空间不零能控的结果． |
| 关键词: 抛物型方程 非局部项 Hm空间 近似能控性 |
| DOI： |
| 分类号:O231.4 |
| 基金项目: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) 和大学生创新创业训练计划省级立项项目 (201910579806). |
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| CONTROLLABILITY OF A CLASS OF PARABOLIC EQUATIONS WITH NON-LOCAL TERMS IN SOBOLEV SPACE |
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ZENG Xi,MO Yu-ling,DENG Zi-juan,LIU Jie,ZHOU Xiu-xiang
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| Abstract: |
| In this paper, we study the controllability problem for a class of parabolic partial differential equations with non-local terms in Hm space. By construction method and duality theory, we conclude that if an integer m is given, a class of the initial value in the Hm 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 L2(0, 1). |
| Key words: parabolic equations non-local term Hm space approximate controllability |
