On optimal location of diffusion and related optimal control for null controllable heat equation

doi:10.1016/j.jmaa.2015.08.023

CSpace > 系统科学研究所

	On optimal location of diffusion and related optimal control for null controllable heat equation
	Guo, Bao-Zhu1,2 ; Yang, Dong-Hui 3; Zhang, Liang 4
	2016-01-15
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	433 期号:2 页码:1333-1349
摘要	We consider optimal locations of heat diffusion and related optimal control to achieve null controllability for multi-dimensional heat equations. Both time optimal control and norm optimal control problems are considered. The reason behind combining these two problems together is that these two problems are actually equivalent: The energy to be used to drive the system to zero in minimal time interval is actually the minimal energy of driving the system to zero in this minimal time interval and visa versa. We formulate the optimal locations for time optimal control and norm optimal control into two types of shape optimization problems. One is seeking the optimal domain of heat diffusion with a fixed interior actuator domain. This can be considered as a domain perturbation problem in shape optimization. Another is to seek both the optimal locations of the optimal heat diffusion domain and the related optimal actuator domain. The existences of these two types of shape optimization problems over some class of open sets in general RN space have been proved separately. (C) 2015 Elsevier Inc. All rights reserved.
关键词	Heat equation Optimal control Shape optimization
DOI	10.1016/j.jmaa.2015.08.023
语种	英语
资助项目	National Natural Science Foundation of China[11371375] ; National Basic Research Program of China[2011CB808002] ; National Research Foundation of South Africa ; Fundamental Research Funds for the Central Universities
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000362048700034
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20889
专题	系统科学研究所
通讯作者	Yang, Dong-Hui
作者单位	1.Acad Sinica, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.Univ Witwatersrand, Sch Comp Sci & Appl Math, ZA-2050 Johannesburg, South Africa 3.Cent S Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China 4.Wuhan Univ Technol, Sch Sci, Wuhan 430070, Peoples R China
推荐引用方式 GB/T 7714	Guo, Bao-Zhu,Yang, Dong-Hui,Zhang, Liang. On optimal location of diffusion and related optimal control for null controllable heat equation[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2016,433(2):1333-1349.
APA	Guo, Bao-Zhu,Yang, Dong-Hui,&Zhang, Liang.(2016).On optimal location of diffusion and related optimal control for null controllable heat equation.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,433(2),1333-1349.
MLA	Guo, Bao-Zhu,et al."On optimal location of diffusion and related optimal control for null controllable heat equation".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 433.2(2016):1333-1349.