Point sources and stability for an inverse problem for a hyperbolic PDE with space and time dependent coefficients

TL;DR

This paper establishes Lipschitz stability results for inverse problems involving point sources in a hyperbolic PDE with space and time-dependent coefficients, using Carleman estimates and a modified Bukgheim-Klibanov method.

Contribution

It introduces a novel stability analysis for inverse hyperbolic problems with point sources and variable coefficients, employing a modified Carleman estimate approach.

Findings

Lipschitz stability for inverse hyperbolic problems with point sources.

Effective use of a modified Bukgheim-Klibanov method.

Applicability to three-dimensional wave equations with variable coefficients.

Abstract

We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we establish Lipschitz stability results for these problems. The main tool in our analysis is a modified version of Bukgheim-Klibanov method based on Carleman estimates.