Nonlocal cross-diffusion systems for multi-species populations and networks

2021/04/13 by Jüngel, Ansgar, Portisch, Stefan, Zurek, Antoine · 1 citation
#35K40 #35K55 #35Q92 #68T07 #92B20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.06292

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.

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