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

Ansgar Jüngel; Stefan Portisch; Antoine Zurek

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arXiv · 2104.06292

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

Ansgar Jüngel·Stefan Portisch·Antoine Zurek

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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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BibTeX RIS

Ansgar Jüngel, Stefan Portisch, Antoine Zurek. 2021-04-13. Nonlocal cross-diffusion systems for multi-species populations and networks. https://arxiv.org/abs/2104.06292

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