Determination of an Unknown Source in the Heat Equation by the Method of Tikhonov Regularization in Hilbert Scales
2014
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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