Stabilizing the nonlinear spherically symmetric backward heat equation via two-parameter regularization method |
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| Authors: | Tra Quoc Khanh Tran Thi Khieu Ngo Van Hoa |
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| Institution: | 1.Faculty of Mathematics and Computer Science,University of Science, Ho Chi Minh City National University,Ho Chi Minh City,Vietnam;2.Department of Scientific Fundamentals,Posts and Telecommunications Institute of Technology,Ho Chi Minh City,Vietnam;3.Division of Computational Mathematics and Engineering Institute for Computational Science,Ton Duc Thang University,Ho Chi Minh City,Vietnam;4.Faculty of Mathematics and Statistics,Ton Duc Thang University,Ho Chi Minh City,Vietnam |
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| 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. |
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