%0 Journal Article
%T Determination of an Unknown Source in the Heat Equation by the Method of Tikhonov Regularization in Hilbert Scales
%A Zhenyu Zhao
%A Ou Xie
%A Zehong Meng
%A Lei You
%J Journal of Applied Mathematics and Physics
%P 10-17
%@ 2327-4379
%D 2014
%I Scientific Research Publishing
%R 10.4236/jamp.2014.22002
%X <p class=\"MsoNormal\" style=\"text-align:justify;\">
	<span lang=\"EN-US\">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</span><span lang=\"EN-US\">-</span><span lang=\"EN-US\">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.</span> 
</p>
%K Ill-Posed Problem
%K Unknown Source
%K Heat Equation
%K Regularization Method
%K Discrepancy Principle in Hilbert Scales
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=42095