Stability Estimates in an Inverse Problem for a Three-Dimensional Heat Equation

Abstract

The problem of determining an insulating body D contained in a conducting one $\Omega $ is studied. If at an initial time the temperature is zero and increasing temperature is assigned on the boundary of $\Omega $ then the knowledge of the flux on a portion of $\partial \Omega $ for a finite interval of time determines D. A logarithmic stability estimate is found if some a priori assumptions are given on $D.$