Nonlocal approximation of an anisotropic cross-diffusion system
Analysis of PDEs
2024-12-31 v1
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.
Cite
@article{arxiv.2412.20188,
title = {Nonlocal approximation of an anisotropic cross-diffusion system},
author = {Tomasz Dębiec and Markus Schmidtchen},
journal= {arXiv preprint arXiv:2412.20188},
year = {2024}
}