Simultaneous determination of source term and initial value in the heat conduction problem by modified quasi-reversibility regularization method

doi:10.1080/10407790.2022.2079281

	Simultaneous determination of source term and initial value in the heat conduction problem by modified quasi-reversibility regularization method
	Wen, Jin 1; Ren, Xue-Juan 1,2; Wang, Shi-Juan3,4
	2022
发表期刊	Numerical Heat Transfer, Part B: Fundamentals
卷号	82 期号:3-4 页码:112-127
摘要	In this article, we investigate the inverse problem of determining source term and initial data simultaneously in a parabolic equation where data are given at two fixed times. We can get the exact solution of the problem by the Fourier transform, and find that the problem is ill-posed, i.e., the solution does not depend continuously on the input data and small errors in the data can destroy the numerical solution. Hence, a modified quasi-reversibility regularization method is used to solve the problem and an order-optimal error estimate is obtained under a suitable parameter choice rule. Finally, some numerical examples including smooth and nonsmooth functions show that the proposed method is effective and stable. © 2022 Northwest Normal University.
关键词	Errors Inverse problems Numerical methods Backward heat conductions Error estimates Heat conduction problems Inverse source Modified quasi-reversibility regularization method Numerical experiments Quasi-reversibility Regularization methods Simultaneous determinations Source terms
DOI	10.1080/10407790.2022.2079281
收录类别	EI ; SCIE
ISSN	1040-7790
语种	英语
WOS研究方向	Thermodynamics ; Mechanics
WOS类目	Thermodynamics ; Mechanics
WOS记录号	WOS:000807633900001
出版者	Taylor and Francis Ltd.
EI入藏号	20222412217944
EI主题词	Heat conduction
EI分类号	641.2 Heat Transfer ; 921.6 Numerical Methods
原始文献类型	Journal article (JA)
EISSN	1521-0626
引用统计	被引频次：8[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.lzufe.edu.cn/handle/39EH0E1M/33211
专题	信息工程与人工智能学院
作者单位	1.Department of Mathematics, Northwest Normal University, Lanzhou, Gansu, China; 2.College of Information Engineering, Tarim University, Xinjiang, Aral, China; 3.School of Traffic and Transportation, Lanzhou Jiaotong University, Gansu, China; 4.School of Information Engineering, Lanzhou University of Finance and Economics, Gansu, China
推荐引用方式 GB/T 7714	Wen, Jin,Ren, Xue-Juan,Wang, Shi-Juan. Simultaneous determination of source term and initial value in the heat conduction problem by modified quasi-reversibility regularization method[J]. Numerical Heat Transfer, Part B: Fundamentals,2022,82(3-4):112-127.
APA	Wen, Jin,Ren, Xue-Juan,&Wang, Shi-Juan.(2022).Simultaneous determination of source term and initial value in the heat conduction problem by modified quasi-reversibility regularization method.Numerical Heat Transfer, Part B: Fundamentals,82(3-4),112-127.
MLA	Wen, Jin,et al."Simultaneous determination of source term and initial value in the heat conduction problem by modified quasi-reversibility regularization method".Numerical Heat Transfer, Part B: Fundamentals 82.3-4(2022):112-127.