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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