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Carleman estimates with no lower-order terms for general Riemann wave equations. Global uniqueness and observability in one shot
Triggiani, R; Yao, PF
2002-09-01
Source PublicationAPPLIED MATHEMATICS AND OPTIMIZATION
ISSN0095-4616
Volume46Issue:2-3Pages:331-375
AbstractThis 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].
KeywordRiemann wave Carleman estimates observability
DOI10.1007/s00245-002-0751-5
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000180114200015
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/17104
Collection中国科学院数学与系统科学研究院
Corresponding AuthorTriggiani, R
Affiliation1.Univ Virginia, Dept Math, Charlottesville, VA 22904 USA
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
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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