确定热方程未知源问题的超阶正则化方法  

A Super Order Regularization Method for Determination of an Unknown Source in the Heat Equation

作　　者：赵振宇 林日光[2] 李志 梅端[2] Zhao Zhenyu;Lin Riguang;Li Zhi;Mei Duan(School of Mathematics and Statistics,Shandong University of Technology,Shandong Zibo 255049;Faculty of Mathematics and Computer Science,Guangdong Ocean University,Guangdong Zhanjiang 524088;Southern Marine Science and Engineering Guangdong Laboratory(Zhanjiang),Guangdong Zhanjiang 524088)

机构地区：[1]山东理工大学数学与统计学院,山东淄博255049 [2]广东海洋大学数学与计算机学院,广东湛江524008 [3]南方海洋科学与工程广东省实验室(湛江),广东湛江524000

出　　处：《数学物理学报（A辑）》2020年第3期717-724,共8页Acta Mathematica Scientia

基　　金：南方海洋科学与工程广东省实验室(湛江)资助项目(ZJW-2019-04);广东海洋大学创新强校工程项目(Q18306)。

摘　　要：该文研究了热传导方程中未知源的确定问题.针对问题的不适定性,提出了一种结合超阶惩罚项的Tikhonov正则化方法.在由偏差原理选取正则化参数情况下,方法能够在不同光滑条件下获得最优收敛阶.计算过程不需要事先知道光滑度和精确解的先验界.数值试验表明,该方法是有效和稳定的.The problem for determining an unknown source in the heat equation is considered in this paper.We present a Tikhonov regularization method with a super order penalty term to deal with illposedness of the problem.The regularization parameter is chosen by a discrepancy principle and the order optimal error bounds can be obtained for various smooth conditions.The smoothness parameter and the a priori bound of exact solution are not needed in the numerical process.Numerical tests show that the proposed method is effective and stable.

关 键 词：不适定问题 超阶正则化 热方程 未知源 偏差原理 

分 类 号：O124[理学—数学]