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

Maria Eckardt; Anna Zhigun

doi:10.1016/j.jmaa.2024.128971

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

Maria Eckardt, Anna Zhigun^*

^*Corresponding author for this work

School of Mathematics and Physics

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Abstract

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 arXiv:2308.05676. The admissible degeneracy of the diffusion tensor is characterised in terms of the upper box fractal dimension.

Original language	English
Article number	128971
Number of pages	22
Journal	Journal of Mathematical Analysis and Applications
Volume	543
Issue number	Issue 2, Part 2
Early online date	22 Oct 2024
DOIs	https://doi.org/10.1016/j.jmaa.2024.128971
Publication status	Published - 15 Mar 2025

Keywords

nonlocal equation
degenerate anisotropic diffusion
non-local diffusion-advection-reaction equation
no-flux boundary conditions

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10.1016/j.jmaa.2024.128971Licence: CC BY

Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion
Copyright 2024 The Authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Final published version, 474 KBLicence: CC BY

Cite this

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title = "Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion",

abstract = "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 arXiv:2308.05676. The admissible degeneracy of the diffusion tensor is characterised in terms of the upper box fractal dimension.",

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AU - Zhigun, Anna

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AB - 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 arXiv:2308.05676. The admissible degeneracy of the diffusion tensor is characterised in terms of the upper box fractal dimension.

KW - nonlocal equation

KW - degenerate anisotropic diffusion

KW - non-local diffusion-advection-reaction equation

KW - no-flux boundary conditions

U2 - 10.1016/j.jmaa.2024.128971

DO - 10.1016/j.jmaa.2024.128971

M3 - Article

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JF - Journal of Mathematical Analysis and Applications

IS - Issue 2, Part 2

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

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Keywords

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