A PARABOLIC INVERSE PROBLEM WITH AN UNKNOWN BOUNDARY-CONDITION

In this paper we consider a parabolic inverse problem in which an unknown function is involved in the boundary condition, and we attempt to recover this function by measuring the value of the temperature at a fixed point on the boundary. The motivation for studying this problem arises from some physical models such as a heat conduction system where the heat exchange between the system and its surrounding is unknown. We apply the singularity estimates for the fundamental solution of a parabolic equation along with the generalized Bellman-Gronwall inequality to obtain the continuous dependence of the solution upon the known data. Uniqueness of the solution is established as a direct corollary. © 1990.