NONLOCAL APPROXIMATION OF AN ANISOTROPIC CROSS-DIFFUSION SYSTEM

作     者：Dębiec, Tomasz Schmidtchen, Markus 

作者机构：INSTITUTE OF APPLIED MATHEMATICS AND MECHANICS UNIVERSITY OF WARSAW BANACHA 2 Warsaw02-097 Poland INSTITUTE OF SCIENTIFIC COMPUTING FACULTY OF MATHEMATICS TU DRESDEN Germany 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Population dynamics 

摘      要：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. Copyright © 2024, The Authors. All rights reserved.