Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems

被引：59

作者：

Lu, Qi ^{[1
,2
]}

机构：

[1] BCAM, Bilbao 48009, Basque Country, Spain

[2] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 610054, Peoples R China

来源：

INVERSE PROBLEMS | 2012年 / 28卷 / 04期

关键词：

BACKWARD UNIQUENESS; DIFFERENTIAL-EQUATIONS; STABILITY; CONTROLLABILITY; COEFFICIENTS;

D O I：

10.1088/0266-5611/28/4/045008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we study two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the history of a stochastic heat process through the observation at the final time T for which we obtain a conditional stability estimate. The other is an inverse source problem with observation on the lateral boundary. We derive the uniqueness of the source.

引用

页数：18

共 30 条

[21] A method for identifying a spacewise-dependent heat source under stochastic noise interference [J].

Johansson, B. Tomas ;

Pricop, Mihaela .

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2010, 18 (01) :51-63

[22]

Klibanov M V., 2004, INVER ILL POSED PROB

[23] INVERSE PROBLEMS AND CARLEMAN ESTIMATES [J].

KLIBANOV, MV .

INVERSE PROBLEMS, 1992, 8 (04) :575-596

[24] Backward uniqueness for solutions of linear parabolic equations [J].

Kukavica, I .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (06) :1755-1760

[25] UNIQUE CONTINUATION FOR PARABOLIC DIFFERENTIAL EQUATIONS AND INEQUALITIES [J].

LEES, M ;

PROTTER, MH .

DUKE MATHEMATICAL JOURNAL, 1961, 28 (03) :369-&

[26]

Pardoux E., 1975, THESIS

[27] Quantitative unique continuation for the semilinear heat equation in a convex domain [J].

Phung, Kim Dang ;

Wang, Gengsheng .

JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (05) :1230-1247

[28] NULL CONTROLLABILITY FOR FORWARD AND BACKWARD STOCHASTIC PARABOLIC EQUATIONS [J].

Tang, Shanjian ;

Zhang, Xu .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (04) :2191-2216

[29] Uniqueness and stability in multidimensional hyperbolic inverse problems [J].

Yamamoto, M .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1999, 78 (01) :65-98

[30] Carleman estimates for parabolic equations and applications [J].

Yamamoto, Masahiro .

INVERSE PROBLEMS, 2009, 25 (12)

← 1 2 3 →