Stability for inverse source problems by Carleman estimates

TL;DR

This paper introduces a simplified method using Carleman estimates to establish conditional stability in inverse source problems for evolution equations, avoiding complex cut-off procedures.

Contribution

The authors develop a modified approach that simplifies existing proofs of stability for inverse source problems in hyperbolic and parabolic equations, broadening applicability.

Findings

Proved conditional stability for hyperbolic inverse source problems.

Extended stability results to parabolic inverse source problems.

Method avoids cut-off procedures, simplifying proofs.

Abstract

In this article, we provide a modified argument for proving conditional stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method needs not any cut-off procedures and can simplify 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.