Recovering a Time-Dependent Diffusion Coefficient From Flux Data in a Fractional Diffusion Model With a Higher-Order Boundary Condition

IF 2 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2026-08-09 Epub Date: 2026-05-19 DOI:10.1002/mma.70802

Bauyrzhan Derbissaly, Medina Kassen, Makhmud Sadybekov, Madi Yergaliyev

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引用次数: 0

Abstract

We study an inverse problem for a time-fractional diffusion equation with a Robin condition at $x = 0$ and an eigenparameter-dependent higher-order boundary condition at $x = 1$ . For the direct problem we prove existence, uniqueness, and regularity of mild solutions. For the inverse recovery of a positive time-varying coefficient $k (t)$ , we introduce a monotone nonlinear operator whose fixed points correspond to data-consistent coefficients. Monotonicity yields uniqueness, and under mild assumptions the associated fixed-point ( $K$ -) iteration is monotone, bounded, and convergent. A modal discretization with L1 time stepping implements the iteration efficiently. Numerical experiments corroborate the theory and examine robustness to noise and the effect of the fractional order $α$ .

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具有高阶边界条件的分数阶扩散模型通量数据恢复随时间的扩散系数

研究了具有Robin条件（x = 0 $$ x=0 $$）和特征参数相关高阶边界条件（x = 1 $$ x=1 $$）的时间分数扩散方程的反问题。对于直接问题，证明了温和解的存在性、唯一性和正则性。对于正时变系数k (t) $$ k(t) $$的逆恢复，我们引入了一个单调非线性算子，其不动点对应于数据一致系数。单调性产生唯一性，并且在温和的假设下，相关的不动点（K $$ K $$ -）迭代是单调的、有界的和收敛的。采用L1时间步进的模态离散化方法有效地实现了迭代。数值实验证实了该理论，并检验了对噪声和分数阶α影响的鲁棒性$$ \alpha $$。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.