Journal of Applied Mathematics and Physics
Volume 2, Issue 2 (January 2014)
ISSN Print: 2327-4352 ISSN Online: 2327-4379
Google-based Impact Factor: 0.70 Citations
Determination of an Unknown Source in the Heat Equation by the Method of Tikhonov Regularization in Hilbert Scales ()
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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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