A strong positivity property and a related inverse source problem for multi-term time-fractional diffusion equations

IF 1.2 4区 数学 Q1 MATHEMATICS Acta Mathematica Scientia Pub Date : 2024-08-27 DOI:10.1007/s10473-024-0523-2
Li Hu, Zhiyuan Li, Xiaona Yang
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引用次数: 0

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.

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多期时间分形扩散方程的强正性属性和相关反源问题
在本文中,我们考虑的是具有多期时间分数导数的扩散方程。我们首先通过解的从属性原理推导出,当初始值为非负时,解为正。作为应用,我们证明了在子域中通过积分型信息确定时变源项的逆问题解的唯一性。最后,我们介绍了几个数值实验,以显示算法的准确性和效率。
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来源期刊
CiteScore
2.00
自引率
10.00%
发文量
2614
审稿时长
6 months
期刊介绍: Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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