On the axisymmetric backward heat equation with non-zero right hand side: Regularization and error estimates

In this paper we consider the time-inverse problem for the axisymmetric heat equation with non-zero right hand side. This problem is ill-posed: the solution (if it exists) does not depend continuously on the final data. We use a modified quasi-boundary value to regularize the inhomogeneous problem. Numerical results are presented to illustrate the accuracy and efficiency of the method.