{
  "abstract": "This paper addresses the approximation of entropy solutions to a one-dimensional scalar conservation law via the so-called Follow-the-Leader particle scheme in case the velocity map is \\emph{non monotone}. The result is based on a discrete maximum principle, on $BV$ estimates of the approximated density, and on the characterization of the limit as entropy solution in the sense of Kru\\v zkov.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.28195",
  "author_total": 1,
  "authors": [
    {
      "name": "Marco Di Francesco"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brabwcjk7t0n9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.28195",
  "fulltext_url": null,
  "id": "brabwcjk7t0n9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.28195",
  "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",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7171980429",
  "pdf_url": "https://arxiv.org/pdf/2607.28195",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brabwcjk7t0n9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2607.28195",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.28195"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Follow-the-Leader scheme with non-monotone velocity",
  "title_text": "The Follow-the-Leader scheme with non-monotone velocity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/brabwcjk7t0n9",
  "venue": "arXiv",
  "versions": []
}