Lipschitz stability in inverse source problems for a singular parabolic equation. Issue 8 (24th May 2022) - Anh, Cung The; Toi, Vu Manh; Tuan, Tran Quoc
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.