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

Authors: 

Tra Quoc Khanh, Ngo Van Hoa*

Source title: 
Journal of Computational and Applied Mathematics, 335: 156-167, 2018 (ISI)
Academic year of acceptance: 
2017-2018
Abstract: 

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.