W.B. Muniz, H.F. Campos Velho and F.M. Ramos (2000): Solution of the Backward Heat Conduction Equation Using Different Regularization Techniques, submitted Computers & Mathematics with Applications. (accepeted)

Abstract: The goal of this paper is to analyse the performance of different regularization techniques for an {\it inverse heat conduction problem} (IHCP): the estimation of the initial condition. The inverse problem is formulated as a nonlinear constrained optimization problem, and a regularization term is added to the objective function with the help of a Lagrange multiplier. Three regularization techniques have been considered: zeroth-order and first-order Tikhonov regularization, and maximum entropy principle. A semi-analytical integral approach is used to handle the corresponding direct problem. Good results were obtained for all regularization functions using synthetic data corrupted with noise.