{
  "abstract": "This work provides a traffic flow interpretation of the model recently introduced in \\cite{ABS2025}. We adapt the conservation law with discontinuous gradient-dependent flux to a macroscopic traffic setting, assuming concave flux functions $f(u)$ and $g(u)$ defined on the density domain $[0,u_{\\max}]$. To prevent violations of the maximal density constraint, we introduce modified Riemann Solvers tailored to this setting and generalize the existence theory for weak solutions developed in \\cite{ABS2025}. Finally, we construct Riemann Solvers for a broader two-phase model incorporating a free-flow regime, in which $f(u)=g(u)$ on a subset of $[0,u_{\\max}]$, and establish existence of weak solutions in this more general framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30859",
  "author_total": 3,
  "authors": [
    {
      "name": "Roberta Bianchini"
    },
    {
      "name": "Maya Briani"
    },
    {
      "name": "Benedetto Piccoli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5tdcysxvkhqjf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30859",
  "fulltext_url": null,
  "id": "5tdcysxvkhqjf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30859",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2207|Traffic control and management"
    ]
  ],
  "openalex": "W7204925810",
  "pdf_url": "https://arxiv.org/pdf/2608.30859",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5tdcysxvkhqjf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30859",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30859"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Conservation Laws with Discontinuous Flux: A First Application to Traffic Flow",
  "title_text": "Conservation Laws with Discontinuous Flux: A First Application to Traffic Flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/5tdcysxvkhqjf",
  "venue": "arXiv",
  "versions": []
}