ON STABILITY AND REGULARIZATION FOR BACKWARD HEAT EQUATION

Consider a backward heat equation in a bounded domain Ω R2 with the noisy data in theinitial time geometry. The aim is to find the temperature for 0 ＜ε＜ t ＜ T. For this ill-posedproblem, the authors give a continuous dependence estimate of the solution. Moreover, theconvergence rate of the approximate solution is also given.