Continuous dependence and uniqueness for lateral Cauchy problems for   linear integro-differential parabolic equations
  Via Carleman estimates we prove uniqueness and continuous dependence results for lateral Cauchy problems for linear integro-differential parabolic equations without initial conditions. The additional information supplied prescribes the conormal derivative of the temperature on a relatively open subset of the lateral boundary of the space-time domain. 
A. Lorenzi, L. Lorenzi, M. Yamamoto
math.AP