Determination of the solution of a stochastic parabolic equation by the terminal value. (1st July 2022)

• Record Type: Journal Article
• Authors: Dou, Fangfang; Du, Wanli
• Is Part Of: Inverse problems. Volume 38:Number 7(2022)
• Publication Date: 2022-07-01
• Subjects: stochastic parabolic equation -- Carleman estimate -- conditional stability -- regularization method; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac72bc
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This paper studies the inverse problem of determination the history for a stochastic diffusion process, by means of the value at the final time T . By establishing a new Carleman estimate, the conditional stability of the problem is proven. Based on the idea of Tikhonov method, a regularized solution is proposed. The analysis of the existence and uniqueness of the regularized solution, and proof for error estimate under an a priori assumption are present. Numerical verification of the regularization, including numerical algorithm and examples are also illustrated.