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Stabilizing the nonlinear spherically symmetric backward heat equation via two-parameter regularization method

Authors: 

Tra Quoc Khanh, Nguyen Thi Khieu, Ngo Van Hoa*

Source title: 
Journal of Fixed Point Theory and Applications, 19(4): 2461-2481, 2017 (ISI)
Academic year of acceptance: 
2017-2018
Abstract: 

In this paper, we consider a time-inverse problem for a nonlinear spherically symmetric backward heat equation which is a severely ill-posed problem. Using a modified integral equation method with two regularization parameters: one related to the error in a measurement process and the other is related to the regularity of solution, we regularize this problem and obtain the Hölder-type estimation error for the whole time interval. Numerical results are presented to illustrate the accuracy and efficiency of the method.