Stability for inverse source problems by Carleman estimates. (3rd December 2020)

• Record Type: Journal Article
• Authors: Huang, X; Yu Imanuvilov, O; Yamamoto, M
• Is Part Of: Inverse problems. Volume 36:Number 12(2020)
• Publication Date: 2020-12-03
• Subjects: inverse source problem -- stability -- Carleman estimate; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aba892
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this article, we provide a modified argument for proving stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method does not require any cut-off procedures and therefore simplifies the existing proofs. We establish the conditional stability for inverse source problems for a hyperbolic equation and a parabolic equation, and our method is widely applicable to various evolution equations.