Determination of an Unknown Source in the Heat Equation by the Method of Tikhonov Regularization in Hilbert Scales

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DOI: 10.4236/jamp.2014.22002    3,734 Downloads   6,269 Views  Citations

ABSTRACT

In this paper, we consider the problem for determining an unknown source in the heat equation. The Tikhonov regularization method in Hilbert scales is presented to deal with ill-posedness of the problem and error estimates are obtained with a posteriori choice rule to find the regularization parameter. The smoothness parameter and the a priori bound of exact solution are not needed for the choice rule. Numerical tests show that the proposed method is effective and stable.

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Zhao, Z. , Xie, O. , Meng, Z. and You, L. (2014) Determination of an Unknown Source in the Heat Equation by the Method of Tikhonov Regularization in Hilbert Scales. Journal of Applied Mathematics and Physics, 2, 10-17. doi: 10.4236/jamp.2014.22002.

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