外域中时间分量扩散方程系统的不存在性

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-19 DOI:10.1002/mma.10489

Mohamed Jleli, Bessem Samet

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引用次数: 0

摘要

本文研究了在同质 Dirichlet 边界条件下，( )外部域中的时间分量扩散方程组。时间分数导数是在卡普托意义上考虑的。利用专门针对卡普托分数导数的非局部特性、域的几何形状和边界条件而调整的非线性容量估计，我们得到了所考虑的系统不存在弱解的充分条件。

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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Nonexistence for a system of time‐fractional diffusion equations in an exterior domain

A system of time‐fractional diffusion equations posed in an exterior domain of ( ) under homogeneous Dirichlet boundary conditions is investigated in this paper. The time‐fractional derivatives are considered in the Caputo sense. Using nonlinear capacity estimates specifically adapted to the nonlocal properties of the Caputo fractional derivative, the geometry of the domain, and the boundary conditions, we obtain sufficient conditions for the nonexistence of a weak solution to the considered system.

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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.