A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS*

doi:10.1007/s10473-024-0523-2

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 2019-2040.doi: 10.1007/s10473-024-0523-2

A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS^*

Li hu¹, Zhiyuan li^1,†, Xiaona yang²

1. School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China;
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

收稿日期:2022-06-23 修回日期:2024-06-05 出版日期:2024-10-25 发布日期:2024-10-22
通讯作者: †Zhiyuan li, E-mail,: lizhiyuan@nbu.edu.cn
作者简介:Li hu, E-mail,: 2211400016@nbu.edu.cn; Xiaona yang, E-mail,: xiaonayang1004@163.com
基金资助:
National Natural Science Foundation of China (12271277) and the Open Research Fund of Key Laboratory of Nonlinear Analysis & Applications (Central China Normal University), Ministry of Education, China.

A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS^*

Li hu¹, Zhiyuan li^1,†, Xiaona yang²

1. School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China;
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received:2022-06-23 Revised:2024-06-05 Online:2024-10-25 Published:2024-10-22
Contact: †Zhiyuan li, E-mail,: lizhiyuan@nbu.edu.cn
About author:Li hu, E-mail,: 2211400016@nbu.edu.cn; Xiaona yang, E-mail,: xiaonayang1004@163.com
Supported by:
National Natural Science Foundation of China (12271277) and the Open Research Fund of Key Laboratory of Nonlinear Analysis & Applications (Central China Normal University), Ministry of Education, China.

摘要/Abstract

摘要： In this article, we consider the diffusion equation with multi-term time-fractional derivatives. We first derive, by a subordination principle for the solution, that the solution is positive when the initial value is non-negative. As an application, we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

关键词: fractional diffusion equation, inverse source problem, nonlocal observation observation, uniqueness, Tikhonov regularization

Abstract: In this article, we consider the diffusion equation with multi-term time-fractional derivatives. We first derive, by a subordination principle for the solution, that the solution is positive when the initial value is non-negative. As an application, we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Key words: fractional diffusion equation, inverse source problem, nonlocal observation observation, uniqueness, Tikhonov regularization

中图分类号:

35K65

Li hu, Zhiyuan li, Xiaona yang. A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS^*[J]. 数学物理学报(英文版), 2024, 44(5): 2019-2040.

Li hu, Zhiyuan li, Xiaona yang. A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS^*[J]. Acta mathematica scientia,Series B, 2024, 44(5): 2019-2040.

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A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS^*

A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS^*

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