Stability estimates for the anisotropic wave equation from the Dirichlet-to-Neumann map

TL;DR

This paper establishes stability estimates for the inverse problem of recovering potential or velocity in an anisotropic wave equation from boundary measurements, proving uniqueness and Hölder stability in dimensions two and higher.

Contribution

It provides the first stability estimates for the anisotropic inverse wave problem using the Dirichlet-to-Neumann map, including uniqueness and Hölder stability results.

Findings

Unique determination of potential from boundary data in dimensions n≥2

Hölder stability estimates for potential recovery

Extension of inverse problem results to anisotropic media

Abstract

In this article we seek stability estimates in the inverse problem of determining the potential or the velocity in a wave equation in an anisotropic medium from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\geq 2$ that the knowledge of the Dirichlet-to-Neumann map for the wave equation uniquely determines the electric potential and we prove H\"older-type stability in determining the potential.