On the local controllability of a class of multidimensional quasilinear parabolic equations

doi:10.1016/j.crma.2009.09.017

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	On the local controllability of a class of multidimensional quasilinear parabolic equations
	Liu, Xu 1,2; Zhang, Xu 2,3
	2009-12-01
发表期刊	COMPTES RENDUS MATHEMATIQUE
ISSN	1631-073X
卷号	347 期号:23-24 页码:1379-1384
摘要	In this Note, we study the local null controllability and the cost estimate for a class of multidimensional quasilinear parabolic equations with homogeneous Dirichlet boundary conditions and an arbitrary located internal controller. Unlike the known result for one space dimension, we need to consider the problem in the frame of classical solutions. The key point is to improve the regularity of control function for smooth data, which is a consequence of a new observability inequality for linear parabolic equations with an explicit estimate on the observability constant in terms of the C(1)-norm of the principle part coefficients. The later is based on a new global Carleman estimate for the linear parabolic equation. To cite this article: X. Liu, X. Zhang, C. R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
DOI	10.1016/j.crma.2009.09.017
语种	英语
资助项目	NSF of China[10826077] ; NSF of China[10901032] ; NSF of China[10601010] ; NSF of China[10525105] ; NSF of China[10831007] ; NSF of China[60821091] ; NSF of China[60974035] ; Cultivation Foundation of Science and Technology Innovation of Northeast Normal University ; Science Foundation for Young Teachers of Northeast Normal University[20080101] ; Spanish Ministry of Science and Innovation[MTM2008-03541] ; Chunhui program[Z007-1-61006]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000272891400011
出版者	ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7799
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Xu
作者单位	1.NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China
推荐引用方式 GB/T 7714	Liu, Xu,Zhang, Xu. On the local controllability of a class of multidimensional quasilinear parabolic equations[J]. COMPTES RENDUS MATHEMATIQUE,2009,347(23-24):1379-1384.
APA	Liu, Xu,&Zhang, Xu.(2009).On the local controllability of a class of multidimensional quasilinear parabolic equations.COMPTES RENDUS MATHEMATIQUE,347(23-24),1379-1384.
MLA	Liu, Xu,et al."On the local controllability of a class of multidimensional quasilinear parabolic equations".COMPTES RENDUS MATHEMATIQUE 347.23-24(2009):1379-1384.