时间分数阶扩散方程中空间相关源项与初值的同时反演

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-02-08 DOI:10.1515/cmam-2022-0058

Shuang Yu, Zewen Wang, Hongqi Yang

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引用次数: 0

摘要

本文研究了同时识别时间分数扩散方程中与空间相关的源项和初值的反问题。基于时间分数扩散方程的傅立叶方法，将同时反演公式化为两个算子方程组。在一些适当的假设下，建立了同时反演解的条件稳定性，并提出了指数Tikhonov正则化方法来获得同时反演解良好的近似值。然后，对于正则化参数的先验和后验选择，给出了反演解的收敛性估计。最后，通过数值实验验证了该方法的有效性。

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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Simultaneous Inversion of the Space-Dependent Source Term and the Initial Value in a Time-Fractional Diffusion Equation

Abstract The inverse problem for simultaneously identifying the space-dependent source term and the initial value in a time-fractional diffusion equation is studied in this paper. The simultaneous inversion is formulated into a system of two operator equations based on the Fourier method to the time-fractional diffusion equation. Under some suitable assumptions, the conditional stability of simultaneous inversion solutions is established, and the exponential Tikhonov regularization method is proposed to obtain the good approximations of simultaneous inversion solutions. Then the convergence estimations of inversion solutions are presented for a priori and a posteriori selections of regularization parameters. Finally, numerical experiments are conducted to illustrate effectiveness of the proposed method.

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.