Superlinear nonlocal diffusion systems for multispecies populations: well-posedness and discrete chain rules
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-Mazón-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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BibTeX
@misc{hirvonen2026superlinear,
title = {{Superlinear nonlocal diffusion systems for multispecies populations: well-posedness and discrete chain rules}},
author = {Peter Hirvonen and Ansgar Jüngel and Annamaria Pollino},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09921},
eprint = {2609.09921},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09921},
}
RIS
TY - UNPB
TI - Superlinear nonlocal diffusion systems for multispecies populations: well-posedness and discrete chain rules
AU - Peter Hirvonen
AU - Ansgar Jüngel
AU - Annamaria Pollino
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09921
UR - https://arxiv.org/abs/2609.09921
AB - 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-Mazón-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.
ER -