KMS Of Academy of mathematics and systems sciences, CAS
| On the local controllability of a class of multidimensional quasilinear parabolic equations | |
| Liu, Xu1,2; Zhang, Xu2,3 | |
| 2009-12-01 | |
| Source Publication | COMPTES RENDUS MATHEMATIQUE
 |
| ISSN | 1631-073X |
| Volume | 347Issue:23-24Pages:1379-1384 |
| Abstract | 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 |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000272891400011 |
| Publisher | ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/7799 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Liu, Xu |
| Affiliation | 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 |
| Recommended Citation 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. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment