具有退化各向异性扩散的非局部方程的全局存在解

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-10-17 DOI:10.1016/j.jmaa.2024.128971

Maria Eckardt , Anna Zhigun

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引用次数: 0

摘要

在高维度无流动边界条件下，建立了非局部扩散-对流-反应方程极弱解的全局存在性。该方程以退化近视扩散和非局部粘附为特征，是最近在 [21] 中推导出的质量守恒模型的扩展。扩散张量的可容许退化性是以上框分形维度来表征的。

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Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion

Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and is an extension of a mass-conserving model recently derived in [21]. The admissible degeneracy of the diffusion tensor is characterised in terms of the upper box fractal dimension.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.