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.

引用

页码：441 / 452

页数：12

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