An inverse Problem for a parabolic System in an unbounded Guide

Abstract:   In this article we consider a two-by-two parabolic system defined on an unbounded guide with coefficients depending both on the space variable and on the time variable. The main aim of this paper is to obtain a stability result for the coefficients depending on the space variable. Using Carleman inequalities adapted for the guide, we obtain Hölder estimates of these coefficients in any finite portion of the guide with boundary measurements, given two sets of initial conditions.