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The revised generalized Tikhonov regularization for the inverse time-dependent heat source problem

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Abstract

This paper investigates the inverse problem of finding a time-dependent heat source in a parabolic equation where the data is given at a fixed location. A conditional stability result is given, and a revised generalized Tikhonov regularization method with error estimate is also provided. Numerical examples show that the regularization method is effective and stable.

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Acknowledgements

We would like to thank the referees for their valuable comments and helpful suggestions to improve the earlier version of the paper.

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Authors and Affiliations

  1. School of Science, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People’s Republic of China

    Fan Yang

  2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People’s Republic of China

    Fan Yang & Chu-Li Fu

Authors
  1. Fan Yang
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  2. Chu-Li Fu
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Corresponding author

Correspondence to Fan Yang.

Additional information

The project is supported by the National Natural Science Foundation of China (No. 11171136) and the Distinguished Young Scholars Fund of Lan Zhou University of Technology (Q201015).

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Yang, F., Fu, CL. The revised generalized Tikhonov regularization for the inverse time-dependent heat source problem. J. Appl. Math. Comput. 41, 81–98 (2013). https://doi.org/10.1007/s12190-012-0596-2

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  • DOI: https://doi.org/10.1007/s12190-012-0596-2

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