Lipschitz stability in inverse source problems for a singular parabolic equation. Issue 8 (24th May 2022)

• Record Type: Journal Article
• Authors: Anh, Cung The; Toi, Vu Manh; Tuan, Tran Quoc
• Is Part Of: Applicable analysis. Volume 101:Issue 8(2022)
• Page Start: 2805
• Page End: 2824
• Publication Date: 2022-05-24
• Subjects: M. Yamamoto; Carleman estimate -- Hardy inequality -- inverse source problem -- Lipschitz stability -- parabolic equation -- inverse-square potential; 34M50 -- 35K67 -- 35A23; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1823374
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study inverse source problems for the heat equation with an inverse-square potential localized on the boundary of a smooth bounded domain, and with a locally distributed observation. We first derive an improved Carleman estimate of that obtained by Cazacu [SIAM J Control Optim. 2014;52:2055–2089] and then use it to prove the Lipschitz stability result for the inverse source problem.