Stability for inverse source problems by Carleman estimates

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. © 2020 IOP Publishing Ltd.