A quasi-boundary value regularization method for the spherically symmetric backward heat conduction problem

Abstract

In this article, we investigate a spherically symmetric backward heat conduction problem, starting from the final temperature. This problem is severely ill posed: the solution (if it exists) does not depend continuously on the final data. A conditional stability result of its solution is given. Further, we propose a quasi-boundary value regularization method to solve this ill-posed problem. Two Hölder type error estimates between the approximate solution and its exact solution are obtained under an a priori and an a posteriori regularization parameter choice rule, respectively.