求解热源识别问题的修正吉洪诺夫正则化方法  

A Modified Tikhonov Regularization Method for Identifying an Unknown Source in the Heat Equation

作　　者：赵振宇[1] 由雷[1] 

机构地区：[1]广东海洋大学理学院

出　　处：《数学物理学报（A辑）》2014年第1期186-192,共7页Acta Mathematica Scientia

基　　金：国家自然科学基金(11201085)资助

摘　　要：该文研究了一个热源识别问题,通过引入修正吉洪诺夫方法来处理问题的不适定性,在一种先验和一种后验参数选取准则下,分别获得了问题的误差估计.数值例子进一步验证了方法的有效性和稳定性.In this paper, we consider the problem for determining the unknown source in the heat equation. A modified Tikhonov regularization method is presented to deal with the illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical tests show that the proposed method is effective and stable. Key words： Ill-posed problem; Unknown crepancy principle; Hilbert scales. source; Heat equation; Regularization method; Dis-

关 键 词：不适定问题 未知源 热方程 正则化方法 偏差原理 

分 类 号：O124[理学—数学]