Analysis of a fractional cross-diffusion system for multi-species populations
Analysis of PDEs
2022-03-21 v2
Abstract
The global in time existence of weak solutions to a cross-diffusion system with fractional diffusion in the whole space is proved. The equations describe the evolution of multi-species populations in the regime of large-distance interactions; they have been derived in the many-particle limit from moderately interacting particle systems with L\'evy noise. The existence proof is based on a three-level approximation scheme, entropy and moment estimates, and a new Aubin-Lions compactness lemma in the whole space.
Cite
@article{arxiv.2202.03787,
title = {Analysis of a fractional cross-diffusion system for multi-species populations},
author = {Ansgar Jüngel and Nicola Zamponi},
journal= {arXiv preprint arXiv:2202.03787},
year = {2022}
}