Uniqueness, stability and numerical reconstruction of a time and space-dependent conductivity for an inverse hyperbolic problem

This paper is devoted to the reconstruction of the time and space-dependent coefficient in an inverse hyperbolic problem in a bounded domain. Using a local Carleman estimate we prove the uniqueness and a H\uf6lder stability in the determination of the conductivity by a single measurement on the lateral boundary. Our numerical examples show possibility of the determination of the location and the large contrast of the space-dependent function in three dimensions