Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations

TL;DR

This paper establishes Lipschitz stability for reconstructing two unknown coefficients in a hyperbolic acoustic equation from interior data, ensuring unique and stable solutions, supported by numerical validation.

Contribution

It introduces a Lipschitz stability estimate for an inverse hyperbolic problem involving two coefficients, using Carleman estimates and numerical validation.

Findings

Lipschitz stability guarantees unique reconstruction.

Numerical studies confirm stability with noisy data.

Method applicable to interior data of hyperbolic equations.

Abstract

We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensures unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the reconstruction of two unknown coefficients using noisy backscattered data.