Numerical recovery of a time-dependent potential in subdiffusion *

IF 2 2区数学 Q1 MATHEMATICS, APPLIED Inverse Problems Pub Date : 2023-12-28 DOI:10.1088/1361-6420/ad14a0

Bangti Jin, Kwancheol Shin, Zhi Zhou

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Abstract

In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian–Caputo fractional derivative in time. Theoretically, we prove a novel conditional Lipschitz stability result, and numerically, we develop an easy-to-implement fixed point iteration for recovering the unknown coefficient. In addition, we establish rigorous error bounds on the discrete approximation. These results are obtained by crucially using smoothing properties of the solution operators and suitable choice of a weighted

Lp(0,T)

norm. The efficiency and accuracy of the scheme are showcased on several numerical experiments in one- and two-dimensions.

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次扩散中与时间相关的势的数值恢复 *

在这项工作中，我们研究了一个逆问题，即从对域内溶液的积分测量中恢复半线性亚扩散模型中与时间相关的势。该模型涉及时间上的 Djrbashian-Caputo 分数导数。在理论上，我们证明了一个新颖的条件 Lipschitz 稳定性结果；在数值上，我们开发了一种易于实现的定点迭代方法，用于恢复未知系数。此外，我们还建立了离散近似的严格误差边界。这些结果主要是利用求解算子的平滑特性和适当选择加权 Lp(0,T) 准则得到的。该方案的效率和准确性在多个一维和二维数值实验中得到了展示。

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

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.