Nonlocal approximation of an anisotropic cross-diffusion system

Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems. This work addresses this gap by establishing the nonlocal-to-limit for a specific anisotropic cross-diffusion system encountered in population dynamics featuring phase-separation phenomena, i.e., internal layers between different species. A critical element of the proof is an entropy dissipation identity, which we show to hold for any weak solution.

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Publication Details

Journal
Nonlinear Analysis
Published
2025-06-02
DOI
https://doi.org/10.1016/j.na.2025.113835
Primary Topic
Advanced Mathematical Modeling in Engineering
Type
article
Field-Weighted Citation Impact
0.00

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article

Nonlocal approximation of an anisotropic cross-diffusion system

Tomasz Dębiec, Markus Schmidtchen
Nonlinear Analysis
Advanced Mathematical Modeling in Engineering
article

Nonlocal approximation of an anisotropic cross-diffusion system

Tomasz Dębiec, Markus Schmidtchen
article en

Abstract

Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems. This work addresses this gap by establishing the nonlocal-to-limit for a specific anisotropic cross-diffusion system encountered in population dynamics featuring phase-separation phenomena, i.e., internal layers between different species. A critical element of the proof is an entropy dissipation identity, which we show to hold for any weak solution.

Nonlinear AnalysisVol. 260
University of Warsaw (PL), Technische Universität Dresden (DE)
Deutscher Akademischer Austauschdienst, Narodowe Centrum Nauki
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Advanced Mathematical Modeling in Engineering
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