Regularization error analysis on a one-dimensional inverse heat conduction problem in multilayer domain

Abstract

We investigate in this paper a non-characteristic Cauchy problem for a one-dimensional heat conduction equation in a multilayer domain, which is a well-known ill-posed problem. We first formulate the Cauchy problem in the frequency domain via Fourier transform technique. A modified version of the classical Tikhonov regularization technique together with the corresponding error estimates is presented. Several numerical examples are constructed to demonstrate the superior efficiency and accuracy of the proposed approach. Numerical results show that the modified Tikhonov regularization technique performs better than the classical Tikhonov regularization technique.