A modified Tikhonov regularization method for a spherically symmetric three-dimensional inverse heat conduction problem

Abstract

This paper deals with a spherically symmetric three-dimensional inverse heat conduction problem of determining the internal surface temperature distribution of a hollow sphere from the measured data at a fixed location inside it. This is an ill-posed problem, i.e., the solution (if it exists) does not depend continuously on the data. A modified Tikhonov regularization method is given and an order optimal stability estimate is obtained.