The quasi-reversibility method for recovering a source in a fractional evolution equation

IF 2.5 2区 数学 Q1 MATHEMATICS
Liangliang Sun, Zhaoqi Zhang, Yunxin Wang
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引用次数: 0

Abstract

In this paper, a quasi-reversibility method is used to solve an inverse spatial source problem of multi-term time-space fractional parabolic equation by observation at the terminal measurement data. We are mainly concerned with the case where the time source can be changed sign, which is practically important but has not been well explored in literature. Under certain conditions on the time source, we establish the uniqueness of the inverse problem, and also a Hölder-type conditional stability of the inverse problem is firstly given. Meanwhile, we prove a stability estimate of optimal order for the inverse problem. Then some convergence estimates for the regularized solution are proved under an a-priori and an a-posteriori regularization parameter choice rule. Finally, several numerical experiments illustrate the effectiveness of the proposed method in one-dimensional case.

分数阶演化方程中恢复源的准可逆性方法
本文利用拟可逆性方法,通过对终端测量数据的观测,解决了多项时空分数抛物方程的空间逆源问题。我们主要关注的是时间源可以变符号的情况,这在现实中很重要,但在文献中还没有得到很好的探讨。在一定的时间源条件下,我们建立了反问题的唯一性,并首次给出了反问题的Hölder-type条件稳定性。同时,证明了反问题最优阶的稳定性估计。然后在先验和后验正则化参数选择规则下证明了正则化解的收敛性估计。最后,通过数值实验验证了该方法在一维情况下的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Fractional Calculus and Applied Analysis
Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
4.70
自引率
16.70%
发文量
101
期刊介绍: Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.
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