Backward uniqueness for parabolic operators with variable coefficients in a half space | |
Wu, Jie1; Zhang, Liqun2 | |
2016-02-01 | |
Source Publication | COMMUNICATIONS IN CONTEMPORARY MATHEMATICS |
ISSN | 0219-1997 |
Volume | 18Issue:1Pages:38 |
Abstract | It is shown that a function u satisfying vertical bar partial derivative(t)u+ Sigma(i,j) partial derivative(i)(a(ij)partial derivative(j)u)vertical bar <= N(vertical bar u vertical bar+vertical bar del u vertical bar), vertical bar u( x, t)vertical bar <= Ne-N| x| 2 in R-+(n) x [0, T] and u(x, 0) = 0 in R-+(n) under certain conditions on {a(ij)} must vanish identically in R-+(n) x [0, T]. The main point of the result is that the conditions imposed on {a(ij)} are of this type: {a(ij)} are Lipschitz and vertical bar del(x)a(ij) (x, t)vertical bar <= E/vertical bar x vertical bar, where E is less than a given number, and the conditions are optimal in some sense. |
Keyword | Carleman estimates backward uniqueness Landis and Oleinik parabolic operator variable coefficient |
DOI | 10.1142/S021919971550011X |
Language | 英语 |
Funding Project | Chinese NSF[10325104] ; innovation program at CAS ; National Basic Research Program of China[2011CB808002] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000369668100002 |
Publisher | WORLD SCIENTIFIC PUBL CO PTE LTD |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/21964 |
Collection | 数学所 |
Corresponding Author | Wu, Jie; Zhang, Liqun |
Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China |
Recommended Citation GB/T 7714 | Wu, Jie,Zhang, Liqun. Backward uniqueness for parabolic operators with variable coefficients in a half space[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS,2016,18(1):38. |
APA | Wu, Jie,&Zhang, Liqun.(2016).Backward uniqueness for parabolic operators with variable coefficients in a half space.COMMUNICATIONS IN CONTEMPORARY MATHEMATICS,18(1),38. |
MLA | Wu, Jie,et al."Backward uniqueness for parabolic operators with variable coefficients in a half space".COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 18.1(2016):38. |
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