Stability estimates and regularization for an inverse heat conduction problem in semi-infinite and finite time intervals

Authors: Heinz W. Engl and P. Manselli

Abstract: The problem of determining the temperature or the heat flux on one end of an interval from temperature measurements on the (insulated) order end is ill-posed. For the cases of a semi-infinite or finitie time-interval, we obtain stability estimates of lograithmic type under simple a-priori assumptions. If we assume more smoothness, we obtain stability estimates of Hölder type via Tikhonov regularization.