Superlinear nonlocal diffusion systems for multispecies populations: well-posedness and discrete chain rules

Peter Hirvonen; Ansgar Jüngel; Annamaria Pollino

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arXiv · 2609.09921

Superlinear nonlocal diffusion systems for multispecies populations: well-posedness and discrete chain rules

Peter Hirvonen·Ansgar Jüngel·Annamaria Pollino

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Abstract

A nonlocal diffusion system describing the dynamics of multi-species populations and approximating the Shigesada-Kawasaki-Teramoto (SKT) model is analyzed in a bounded domain. The model consists of a system of integro-differential equations of Andreu-Maz\'on-Rossi-Toledo type, in which a nonlocal cross-diffusion operator acts on nonlinear diffusion potentials. We establish the global existence and uniqueness of strong solutions. The existence proof relies on suitable a priori estimates derived from an entropy inequality, whose proof requires the development of novel discrete chain-rule inequalities. As a by-product, these inequalities provide the basis for the construction of structure-preserving finite-volume schemes for the corresponding local SKT system. Uniqueness of solutions is established by means of a duality argument. Finally, one-dimensional numerical simulations illustrate the nonlocal-to-local limit and the qualitative behavior of solutions for superlinear and sublinear diffusion potentials.

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Peter Hirvonen, Ansgar Jüngel, Annamaria Pollino. 2026-09-09. Superlinear nonlocal diffusion systems for multispecies populations: well-posedness and discrete chain rules. https://arxiv.org/abs/2609.09921

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