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

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摘要

In this paper we investigate a problem of the identification of an unknown source from one supplementary temperature measurement at a given instant of time for the transient heat equation. Under an a priori condition we answer the question concerning the best possible accuracy for the problem. The Fourier regularization method is utilized for solving the problem, and its convergent rate is analyzed. Numerical results are presented to illustrate the accuracy and efficiency of the method.

论文关键词:Ill-posed problem,Optimal error bound,Unknown source,Heat equation,Fourier regularization

论文评审过程:Received 24 July 2007, Revised 28 July 2008, Available online 20 January 2009.

论文官网地址:https://doi.org/10.1016/j.cam.2009.01.008