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Abstract
In this article, we consider an inverse problem of determining an unknown heat source term from the final temperature history of the radial domain. This problem is ill-posed: the solution (if it exists) does not depend continuously on the final data. A spectral method is applied to formulate a regularized solution and a logarithmic-type error estimate for the regularized solution is given under a suitable choice of regularization parameter. Numerical results are presented to illustrate the accuracy and efficiency of the method. Meanwhile, the uniqueness of solution for the problem is provided.
Acknowledgements
The authors would like to present great thanks to the referees for their valuable comments and suggestions. The work is supported by the National Natural Science Foundation of China (No. 11171136), the Fundamental Research Fund for Natural Science of Education, Department of Henan Province of China (No. 2009B110007), the Hight-level Personnel Fund of Henan University of Technology (No. 2007BS028), the Natural Science Foundation of Henan Province of China (No. 102300410118) and the Natural Science Foundations of Henan University of Technology (No. 10XZP006; No. 09XZZ038).