Recovering a Constant in a Strongly Ill-Posed Integrodifferential Parabolic Problem
We recover a constant in a strongly ill-posed linear integro-differential parabolic problem with no initial condition, when two boundary conditions are given. The first prescribes the temperature u on the whole of the lateral boundary of the space-time domain, while the latter assigns the conormal derivative of u on an open subset of the lateral boundary. Finally, a linear integral condition involving u is supplied to recover the unknown constant. More precisely, via Carleman estimates we prove uniqueness and continuous dependence results for our strongly ill-posed identification problem.