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A modified Tikhonov regularization method for an axisymmetric backward heat equation

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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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Authors and Affiliations

  1. College of Science, He’nan University of Technology, Zhengzhou, 450001, P. R. China

    Wei Cheng

  2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P. R. China

    Chu Li Fu

Authors
  1. Wei Cheng
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  2. Chu Li Fu
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Correspondence to Chu Li Fu.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 10671085), Fundamental Research Fund for Natural Science of Education Department of He’nan Province of China (Grant No. 2009B110007) and Hight-level Personnel fund of He’nan University of Technology (Grant No. 2007BS028)

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Cheng, W., Fu, C.L. A modified Tikhonov regularization method for an axisymmetric backward heat equation. Acta. Math. Sin.-English Ser. 26, 2157–2164 (2010). https://doi.org/10.1007/s10114-010-8509-5

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  • DOI: https://doi.org/10.1007/s10114-010-8509-5

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