The Quasi-Boundary Value Method for Identifying the Initial Value of the Space-Time Fractional Diffusion Equation

doi:10.1007/s10473-020-0304-5

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	The Quasi-Boundary Value Method for Identifying the Initial Value of the Space-Time Fractional Diffusion Equation
	Yang, Fan; Zhang, Yan; Liu, Xiao; Li, Xiaoxiao
	2020-05
发表期刊	ACTA MATHEMATICA SCIENTIA
ISSN	0252-9602
卷号	40 期号:3 页码:641-658
摘要	In this article, we consider to solve the inverse initial value problem for an inhomogeneous space-time fractional diffusion equation. This problem is ill-posed and the quasi-boundary value method is proposed to deal with this inverse problem and obtain the series expression of the regularized solution for the inverse initial value problem. We prove the error estimates between the regularization solution and the exact solution by using an a priori regularization parameter and an a posteriori regularization parameter choice rule. Some numerical results in one-dimensional case and two-dimensional case show that our method is efficient and stable.
关键词	Space-time fractional diffusion equation Ill-posed problem quasi-boundary value method identifying the initial value
DOI	10.1007/s10473-020-0304-5
收录类别	SCIE
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000534239700004
出版者	SPRINGER
来源库	WOS
引用统计	被引频次：17[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://ir.lut.edu.cn/handle/2XXMBERH/155202
专题	理学院马克思主义学院
通讯作者	Yang, Fan
作者单位	Lanzhou Univ Technol, Dept Math, Lanzhou 730050, Peoples R China
第一作者单位	理学院
通讯作者单位	理学院
第一作者的第一单位	理学院
推荐引用方式 GB/T 7714	Yang, Fan,Zhang, Yan,Liu, Xiao,et al. The Quasi-Boundary Value Method for Identifying the Initial Value of the Space-Time Fractional Diffusion Equation[J]. ACTA MATHEMATICA SCIENTIA,2020,40(3):641-658.
APA	Yang, Fan,Zhang, Yan,Liu, Xiao,&Li, Xiaoxiao.(2020).The Quasi-Boundary Value Method for Identifying the Initial Value of the Space-Time Fractional Diffusion Equation.ACTA MATHEMATICA SCIENTIA,40(3),641-658.
MLA	Yang, Fan,et al."The Quasi-Boundary Value Method for Identifying the Initial Value of the Space-Time Fractional Diffusion Equation".ACTA MATHEMATICA SCIENTIA 40.3(2020):641-658.