Unique continuation and continuous dependence results for a severely ill-posed integro-differential parabolic problem
Alfredo Lorenzi, Francesca Messina · Journal of Inverse and Ill-Posed Problems · 2012
Abstract. Via Carleman estimates we determine sufficient conditions ensuring uniqueness and continuous dependence results for a severely ill-posed linear integro-differential boundary-value parabolic problem with no initial condition. This latter condition is replaced with an additional boundary information prescribing the temperature on an open subset of the geometric domain . The integral operators entering the equation are defined by integrals of Volterra type with respect to time.