Two regularization methods for an axisymmetric inverse heat conduction problem

摘要

We consider an axisymmetric inverse heat conduction problem of determining the surface temperature from a fixed location inside a cylinder. The problem is ill-posed: the solution ( if it exists) does not depend continuously on the data. A modified Tikhonov regularization method and a Fourier regularization method are applied to formulate regularized solutions, which are stably convergent to the exact ones with order optimal error estimates.