Nonlocal cross-diffusion systems for multi-species populations and networks. (June 2022)

• Record Type: Journal Article
• Authors: Jüngel, Ansgar; Portisch, Stefan; Zurek, Antoine
• Is Part Of: Nonlinear analysis. Volume 219(2022)
• Publication Date: 2022-06
• Subjects: 35K40 -- 35K55 -- 35Q92 -- 68T07 -- 92B20; Cross diffusion -- Neural network dynamics -- Entropy method -- Localization limit -- Global existence of solutions -- Weak–strong uniqueness; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112800
• Languages: English
• ISSNs: 0362-546X

Abstract

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 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, only integrable kernels. The associated local cross-diffusion system, derived in the localization limit, is also discussed.