On a backward heat problem with time-dependent coefficient: Regularization and error estimates

Abstract

In this paper, we consider a homogeneous backward heat conduction problem which appears in some applied subjects. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the final data. A new regularization method is applied to formulate regularized solutions which are stably convergent to the exact ones with Holder estimates. A numerical example shows that the computational effect of the method is all satisfactory.