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

  • Li hu ,
  • Zhiyuan li ,
  • Xiaona yang
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  • 1. School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China;
    2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
Li hu, E-mail,: 2211400016@nbu.edu.cn; Xiaona yang, E-mail,: xiaonayang1004@163.com

Received date: 2022-06-23

  Revised date: 2024-06-05

  Online published: 2024-10-22

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.

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.

Cite this article

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 . DOI: 10.1007/s10473-024-0523-2

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