Nonlocal cross-diffusion systems for multi-species populations and networks
Analysis of PDEs
2021-09-28 v2
Abstract
Nonlocal cross-diffusion systems on the torus, arising in population dynamics and neuroscience, are analyzed. The global existence of weak solutions, the weak-strong uniqueness, and the localization limit are proved. The kernels are assumed to be positive definite and in detailed balance. The proofs are based on entropy estimates coming from Shannon-type and Rao-type entropies, while the weak-strong uniqueness result follows from the relative entropy method. The existence and uniqueness theorems hold for nondifferentiable kernels. The associated local cross-diffusion system, derived in the localization limit, is also discussed.
Cite
@article{arxiv.2104.06292,
title = {Nonlocal cross-diffusion systems for multi-species populations and networks},
author = {Ansgar Jüngel and Stefan Portisch and Antoine Zurek},
journal= {arXiv preprint arXiv:2104.06292},
year = {2021}
}