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arXiv · 2412.20188

Nonlocal approximation of an anisotropic cross-diffusion system

Tomasz Dębiec·Markus Schmidtchen
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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.

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Tomasz Dębiec, Markus Schmidtchen. 2024-12-28. Nonlocal approximation of an anisotropic cross-diffusion system. https://arxiv.org/abs/2412.20188

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