# Optimal stability for a first order coefficient in a non-self-adjoint wave equation from dirichlet-to-neumann map

## TL;DR

This paper establishes a Hölder stability estimate for recovering a first order coefficient in a non-self-adjoint wave equation from boundary measurements, advancing inverse problem theory for hyperbolic PDEs.

## Contribution

It provides the first Hölder stability result for this inverse problem in dimensions greater than two, using Carleman estimates and reduction techniques.

## Key findings

- Hölder stability estimate proven for the inverse problem
- Reduction to electromagnetic wave equation inverse problem
- Use of Carleman estimates in the proof

## Abstract

This paper is focused on the study of an inverse problem for a non-self-adjoint hyperbolic equation. More precisely, we attempt to stably recover a first order coefficient appearing in a wave equation from the knowledge of Neumann boundary data. We show in dimension n greater than two, a stability estimate of H{\"o}lder type for the inverse problem under consideration. The proof involves the reduction to an auxiliary inverse problem for an electromagnetic wave equation and the use of an appropriate Carleman estimate.