{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09921",
  "author_total": 3,
  "authors": [
    {
      "name": "Peter Hirvonen"
    },
    {
      "name": "Ansgar Jüngel"
    },
    {
      "name": "Annamaria Pollino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/26j0bvhxtj24h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09921",
  "fulltext_url": null,
  "id": "26j0bvhxtj24h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09921",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7212151110",
  "pdf_url": "https://arxiv.org/pdf/2609.09921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/26j0bvhxtj24h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Superlinear nonlocal diffusion systems for multispecies populations: well-posedness and discrete chain rules",
  "title_text": "Superlinear nonlocal diffusion systems for multispecies populations: well-posedness and discrete chain rules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/26j0bvhxtj24h",
  "venue": "arXiv",
  "versions": []
}