Regularization strategies for a two-dimensional inverse heat conduction problem

Abstract

We consider a two-dimensional inverse heat conduction problem for a slab. This is a severely ill-posed problem. Two regularization strategies, one based on the modification of the equation, the other based on the truncation of high frequency components, are proposed to solve the problem in the presence of noisy data. Error estimates show that the regularized solution is dependent continuously on the data and is an approximation of the exact solution of the two-dimensional inverse heat conduction problem. The relation of these two and other regularization strategies is also discussed.