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Optimal error bound and generalized Tikhonov regularization for identifying an unknown source in the heat equation

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Abstract

In this note we prove a stability estimate for an inverse heat source problem. Based on the obtained stability estimate, we present a generalized Tikhonov regularization and obtain the error estimate. Numerical experiment shows that the generalized Tikhonov regularization works well.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xianning University, Xianning, Hubei, 437100, People’s Republic of China

    Ailin Qian

  2. School of Chemistry and life science, Xianning University, Xianning, Hubei, 437100, People’s Republic of China

    Yan Li

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  1. Ailin Qian
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  2. Yan Li
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Correspondence to Ailin Qian.

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Qian, A., Li, Y. Optimal error bound and generalized Tikhonov regularization for identifying an unknown source in the heat equation. J Math Chem 49, 765–775 (2011). https://doi.org/10.1007/s10910-010-9774-3

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  • DOI: https://doi.org/10.1007/s10910-010-9774-3

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