Inverse moving point source problem for the wave equation

TL;DR

This paper addresses the inverse problem of locating a moving point source in a 3D wave equation using boundary data, establishing uniqueness and stability of the solution.

Contribution

It demonstrates that boundary measurements at six points over finite time uniquely determine the source's trajectory and provides a Lipschitz stability estimate.

Findings

Unique determination of the moving source's trajectory from boundary data.

Lipschitz stability estimate for the inverse problem.

Boundary measurements at six points suffice for reconstruction.

Abstract

In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different points of the boundary over a finite time interval is sufficient to determine uniquely its trajectory. We also derive a Lipschitz stability estimate for the inversion.