{
  "abstract": "We consider the dynamics of an idealised cross-diffusion model of biological invasion in which the diffusion of an invading population is inhibited by a resident population, which is in turn degraded by the former. We formulate and numerically solve the problem that describes the self-similar smoothing of an initially piecewise-constant invading population. In the limit the height ahead of the initial discontinuity vanishes, the speed of propagation also vanishes, but only logarithmically slowly. This result is confirmed by a matched asymptotic analysis. The singular nature of this limit indicates that the system does not permit the existence of compactly supported solutions that exhibit a moving front or interface, which has important implications for the simulation of more complex models that also feature this degenerate diffusive mechanism.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.15228",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael C. Dallaston"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2pfpmmftta2qx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.15228",
  "fulltext_url": null,
  "id": "2pfpmmftta2qx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.15228",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7164934035",
  "pdf_url": "https://arxiv.org/pdf/2606.15228",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2pfpmmftta2qx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2606.15228",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.15228"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Self-similar smoothing of a discontinuity by degenerate cross-diffusion",
  "title_text": "Self-similar smoothing of a discontinuity by degenerate cross-diffusion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/2pfpmmftta2qx",
  "venue": "arXiv",
  "versions": []
}