A modified Tikhonov regularization method for an axisymmetric backward heat equation |
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Authors: | Wei Cheng Chu Li Fu |
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Affiliation: | 1. College of Science, He’nan University of Technology, Zhengzhou, 450001, P. R. China 2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P. R. China
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Abstract: | This paper deals with the inverse time problem for an axisymmetric heat equation. The problem is ill-posed. A modified Tikhonov regularization method is applied to formulate regularized solution which is stably convergent to the exact one. Meanwhile, a logarithmic-Hölder type error estimate between the approximate solution and exact solution is obtained by introducing a rather technical inequality and improving a priori smoothness assumption. |
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Keywords: | Ill-posed problem axisymmetric backward heat equation regularization error estimate |
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