TITLE:
Determination of an Unknown Source in the Heat Equation by the Method of Tikhonov Regularization in Hilbert Scales
AUTHORS:
Zhenyu Zhao, Ou Xie, Zehong Meng, Lei You
KEYWORDS:
Ill-Posed Problem; Unknown Source; Heat Equation; Regularization Method; Discrepancy Principle in Hilbert Scales
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.2,
January
17,
2014
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.