{
  "abstract": "This paper establishes the global existence of classical solutions to the initial-boundary value problem for the planar four-velocity Broadwell model in a multidimensional setting. While uniqueness was already established in our previous work (which addressed existence under the assumption of sufficiently small, bounded, and $C^{1}$-regular initial and boundary data), the objective of the present study is to completely lift this size restriction. By extending the previously developed fixed-point framework, we prove that the methodology remains highly effective for arbitrary initial and boundary data. Within this generalized setting, both the solutions and their first-order partial derivatives are shown to be well-defined and to exist globally for all times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22736",
  "author_total": 2,
  "authors": [
    {
      "name": "Koudzo Togbévi Selom Sobah"
    },
    {
      "name": "Amah Séna D'Almeida"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aasv4r5gm71hf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22736",
  "fulltext_url": null,
  "id": "aasv4r5gm71hf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22736",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7214043964",
  "pdf_url": "https://arxiv.org/pdf/2609.22736",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aasv4r5gm71hf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22736",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22736"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global existence and uniqueness for the planar four-velocity Broadwell model with arbitrary $C^{1}$ bounded initial and boundary data in a rectangular domain",
  "title_text": "Global existence and uniqueness for the planar four-velocity Broadwell model with arbitrary C^1 bounded initial and boundary data in a rectangular domain",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/aasv4r5gm71hf",
  "venue": "arXiv",
  "versions": []
}