The Stable Solution Of Two Inverse Heat Conduction Problems

The aim of this thesis is to study the Regularization Method for stable solution of two inverse heat conduction problems and study their numerical implements.For the one dimensional inverse heat conduction problem,we employ a new Regularization Method (Mollification Method) to find its stable solution.It consists of analysising the ill-posed property by means of Fourier Transform,geting its stable solution through constructing the Mollificator and offering the error estimate of the Mollification solution and the procedure of numerical implement.For the two dimensional inverse heat conduction problem,we employ the famous Tikhonov regularization method to seek its stable numerical solution.We cut the integral kernal given by a infinite series,then discrete and regularize the problem.The numerical experiment under the environment of Matlab is also made.Theoretical and numerical test indicate that the treatment of regularization not only is feasible but also possess the advantages of good numerical stability and high-efficiency.