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

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.