Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary

TL;DR

This paper addresses the inverse problem of recovering waveguide conductivity in a hyperbolic equation using a single boundary measurement, establishing stability via a specialized Carleman estimate.

Contribution

It introduces a novel stability result for the inverse conductivity problem in hyperbolic waveguides using a new Carleman estimate.

Findings

Proves Hölder stability for the inverse problem.

Develops a Carleman estimate tailored for hyperbolic waveguides.

Demonstrates the feasibility of conductivity reconstruction from minimal boundary data.

Abstract

We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove H{\"o}lder stability with the aid of a Carleman estimate specifically designed for hyperbolic waveguides.