A Tikhonov Regularization Method for Solving an Inverse Heat Source Problem

被引：2
|
作者：
Yang, Shuping [1 ]
Xiong, Xiangtuan [1 ]
机构：
[1] Northwest Normal Univ, Dept Math, Lanzhou, Peoples R China
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2020年 / 43卷 / 01期
关键词：
Inverse problems; Ill-posed problems; Heat source; Regularization; Numerical differentiation; NUMERICAL-SOLUTION; CONDITIONAL STABILITY; IDENTIFICATION; EQUATIONS;
D O I：
10.1007/s40840-018-0693-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper deals with the inverse problem of determining a space-wise-dependent heat source in the heat equation. This problem is ill-posed and we apply a Tikhonov regularization method to solve it. The existence and uniqueness of the minimizer of the Tikhonov regularization functional are firstly proved. By an optimal control method, we can obtain a stable solution. The numerical results show that our proposed procedure yields stable and accurate approximation.
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页码：441 / 452
页数：12
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