Carleman estimates with no lower-order terms for general Riemann wave equations. Global uniqueness and observability in one shot | |
Triggiani, R; Yao, PF | |
刊名 | APPLIED MATHEMATICS AND OPTIMIZATION |
2002-09-01 | |
卷号 | 46期号:2-3页码:331-375 |
关键词 | Riemann wave Carleman estimates observability |
ISSN号 | 0095-4616 |
DOI | 10.1007/s00245-002-0751-5 |
英文摘要 | This paper considers a fully general (Riemann) wave equation on a finite-dimensional Riemannian manifold, with energy level (H(1) x L(2)) -terms, under essentially minimal smoothness assumptions on the variable (in time and space) coefficients. The paper provides Carleman-type inequalities: first pointwise, for C(2)- solutions, then in integral form for H(1,1)(Q)-solutions. The aim of the present approach is to provide Carleman inequalities which do not contain lower-order terms, a distinguishing feature over most of the literature. Accordingly, global uniqueness results for overdetermined problems as well as Continuous Observability/Uniform Stabilization inequalities follow in one shot, as a part of the same stream of arguments. Constants in the estimates are, therefore, generally explicit. The paper emphasizes the more challenging pure Neumann B.C. case. The paper is a generalization from the Euclidean to the Riemannian setting of [LTZ] in the more difficult case of purely Neumann B.C., and of [KK1] in the case of Dirichlet B.C. The approach is Riemann geometric, but different from-indeed, more flexible than-the one in [LTY1]. |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | SPRINGER |
WOS记录号 | WOS:000180114200015 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/17103] |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Triggiani, R |
作者单位 | 1.Univ Virginia, Dept Math, Charlottesville, VA 22904 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China |
推荐引用方式 GB/T 7714 | Triggiani, R,Yao, PF. Carleman estimates with no lower-order terms for general Riemann wave equations. Global uniqueness and observability in one shot[J]. APPLIED MATHEMATICS AND OPTIMIZATION,2002,46(2-3):331-375. |
APA | Triggiani, R,&Yao, PF.(2002).Carleman estimates with no lower-order terms for general Riemann wave equations. Global uniqueness and observability in one shot.APPLIED MATHEMATICS AND OPTIMIZATION,46(2-3),331-375. |
MLA | Triggiani, R,et al."Carleman estimates with no lower-order terms for general Riemann wave equations. Global uniqueness and observability in one shot".APPLIED MATHEMATICS AND OPTIMIZATION 46.2-3(2002):331-375. |
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