Well-Posedness of a Semilinear Fractional Diffusion Equation With Caputo Derivative and Special Boundary Conditions

IF 2 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2026-07-24 Epub Date: 2026-04-10 DOI:10.1002/mma.70744

Zakaria Hamdi, Lamine Bouzettouta

引用次数: 0

Abstract

We study a semilinear time-fractional diffusion equation in one spatial dimension, where the time derivative is understood in the sense of Caputo. The problem is complemented with suitable boundary conditions, possibly of moving type. We establish the existence, uniqueness, and regularity of weak solutions under natural assumptions on the data and nonlinearities. The analysis relies on fractional calculus tools, including estimates for the Mittag–Leffler function and a fractional Grönwall inequality. Extensions to nonlinear boundary conditions and moving interfaces are also discussed.

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一类具有Caputo导数和特殊边界条件的半线性分数扩散方程的适定性

我们研究了一维空间上的一个半线性时间分数扩散方程，其中时间导数在卡普托意义上被理解。该问题补充了合适的边界条件，可能是移动型的。在数据和非线性的自然假设下，我们建立了弱解的存在唯一性和正则性。分析依赖于分数阶微积分工具，包括对Mittag-Leffler函数和分数阶Grönwall不等式的估计。对非线性边界条件和运动界面的扩展也进行了讨论。

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

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.