THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION

doi:10.1007/s10473-020-0304-5

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 641-658.doi: 10.1007/s10473-020-0304-5

THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION

杨帆, 张燕, 刘霄, 李晓晓

Department of Mathematics, Lanzhou University of Technology, Lanzhou 730050, China

收稿日期:2019-09-04 出版日期:2020-06-25 发布日期:2020-07-17
作者简介:Fan YANG,E-mail:yfggd114@163.com;Yan ZHANG,E-mail:yanzhanglut@163.com;Xiao LIU,E-mail:liuxiaolut@163.com;Xiaoxiao LI,E-mail:lixiaoxiaogood@126.com
基金资助:
The project is supported by the National Natural Science Foundation of China (11561045, 11961044) and the Doctor Fund of Lan Zhou University of Technology.

THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION

Fan YANG, Yan ZHANG, Xiao LIU, Xiaoxiao LI

Department of Mathematics, Lanzhou University of Technology, Lanzhou 730050, China

Received:2019-09-04 Online:2020-06-25 Published:2020-07-17
Supported by:
The project is supported by the National Natural Science Foundation of China (11561045, 11961044) and the Doctor Fund of Lan Zhou University of Technology.

摘要/Abstract

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

Abstract: 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.

Key words: Space-time fractional diffusion equation, Ill-posed problem, quasi-boundary value method, identifying the initial value

中图分类号:

35R25

杨帆, 张燕, 刘霄, 李晓晓. THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION[J]. 数学物理学报(英文版), 2020, 40(3): 641-658.

Fan YANG, Yan ZHANG, Xiao LIU, Xiaoxiao LI. THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION[J]. Acta mathematica scientia,Series B, 2020, 40(3): 641-658.

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THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION

THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION

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