Uniqueness and stability of time and space-dependent conductivity in a hyperbolic cylindrical domain

TL;DR

This paper establishes the uniqueness and stability of reconstructing a time and space-dependent conductivity in a hyperbolic cylindrical domain using boundary measurements, supported by numerical examples demonstrating effective reconstruction.

Contribution

The paper introduces a novel approach employing local Carleman estimates to prove uniqueness and stability for conductivity reconstruction in a hyperbolic domain.

Findings

Proves uniqueness of conductivity reconstruction with a single boundary measurement.

Establishes Hölder stability for the inverse problem.

Numerical examples demonstrate accurate 3D conductivity reconstruction.

Abstract

This paper is devoted to the reconstruction of the time and space-dependent coefficient in an infinite cylindrical hyperbolic domain. Using a local Carleman estimate we prove the uniqueness and a H\"older stability in the determining of the conductivity by a single measurement on the lateral boundary. Our numerical examples show good reconstruction of the location and contrast of the conductivity function in three dimensions.