Conditional stability in determination of initial data for stochastic parabolic equations. (20th February 2017)

• Record Type: Journal Article
• Authors: Yuan, Ganghua
• Is Part Of: Inverse problems. Volume 33:Number 3(2017:Mar.)
• Publication Date: 2017-02-20
• Subjects: stochastic parabolic equation -- backward heat problem -- conditional stability -- Carleman estimate; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa5d7a
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we solve two kinds of inverse problems in determination of the initial data for stochastic parabolic equations. One is determination of the initial data by lateral boundary observation on arbitrary portion of the boundary, the second one is determination of the initial data by internal observation in a subregion inside the domain. We obtain conditional stability for the two kinds of inverse problems. To prove the results, we estimate the initial data by a terminal observation near the initial time, then we estimate this terminal observation by lateral boundary observation on arbitrary portion of the boundary or internal observation in a subregion inside the domain. To achieve those goals, we derive several new Carleman estimates for stochastic parabolic equations in this paper.