Classical Regularization Methods For An Inverse Heat Conduction Problem On A Two-layer Sphere Domain

In this paper, we study an inverse heat conduction equation in a two-layer sphere domain, this is an ill-posed problem in the sense that the solution does not depend continuously on the original data. The main work of this paper is to apply two classical regularization methods:modified Tikhonov regularization method and Fourier truncation method, to recover the stability of solution.First, we give the formulation of the radially heat equation in multilayer do-main and show the ill-posedness of the problem by obtaining the solution via Fourier transform technique; then we apply modified Tikhonov regularization method to for-mulate regularized solution which is stably convergent to the exact one and obtain the error estimate with suitable choices of regularization parameters under the con-dition of a priori, we also get the corresponding error estimates by introducing a stronger a-priori assumption for the case r= R. Finally, Fourier truncation method is used to solve the problem and the error estimates are proved.