Inverse source problem for a hyperbolic equation by Carleman estimates

TL;DR

This paper introduces a simplified method using Carleman estimates to establish the conditional stability of inverse source problems for hyperbolic equations, avoiding the need for solution extension in time.

Contribution

The paper presents a modified approach that simplifies existing proofs of stability for inverse source problems in hyperbolic equations, applicable to various evolution equations.

Findings

Provides a new proof technique using Carleman estimates

Eliminates the need for solution extension in time

Applicable to a broad class of evolution equations

Abstract

In this article, we provide a modified argument for proving the conditional stability of inverse source problem for a hyperbolic equation. Our method does not require any extension of solution with respect to time and therefore simplifies the existing proofs, which is widely applicable to various evolution equations.