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

作　　者：Zhenyu Zhao Ou Xie Zehong Meng Lei You 

机构地区：[1]College of Science, Guangdong Ocean University, Zhanjiang, China [2]School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, China

出　　处：《Journal of Applied Mathematics and Physics》2014年第2期10-17,共8页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：ILL-POSED Problem UNKNOWN SOURCE Heat Equation Regularization METHOD DISCREPANCY Principle in HILBERT Scales 

分 类 号：O1[理学—数学]