Cross-diffusion limits in multispecies kinetic models
Analysis of PDEs
2025-09-18 v1
Abstract
Cross-diffusion systems are formally derived from multispecies kinetic models in the diffusion limit. The first limit in the multispecies BGK model of Gross and Krook leads to a variant of the non-isothermal Maxwell-Stefan equations. The second limit in a BGK model with Brinkman-type force term yields generalized Busenberg-Travis equations, which reduce for constant temperature to the classical Busenberg-Travis system for segregating population species. Entropy equalities are derived for the kinetic and cross-diffusion equations.
Cite
@article{arxiv.2509.14046,
title = {Cross-diffusion limits in multispecies kinetic models},
author = {Ansgar Jüngel and Annamaria Pollino and Satoshi Taguchi},
journal= {arXiv preprint arXiv:2509.14046},
year = {2025}
}