{
  "abstract": "We rigorously establish the well-posedness of the initial-boundary value problem (IBVP) for the Burgers' equation on the half-line for data in Sobolev-type spaces. The formal solution to this problem was previously derived via the Cole-Hopf transformation and the Fokas unified transform method under the assumption of smooth, Schwartz-class data. In this work, we prove the validity of this formal representation for initial data $u_0\\in \\tilde{H}^{s+1}_x (0,\\infty)$ and boundary data $g_0 \\in H_t^{{(2s+1)}/{4}}$ where $1/2<s<3/2$. Well-posedness is established under two complementary conditions: (1) sufficiently small initial and boundary data, and (2) non-positive boundary data of arbitrary size. The latter condition utilizes the strong minimum principle for the corresponding linear heat equation to ensure the global invertibility of the nonlinear Cole-Hopf map. The proofs combine linear estimates for the heat IBVP with nonlinear bounds obtained through Taylor series representations and the algebraic properties of Sobolev spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33886",
  "author_total": 2,
  "authors": [
    {
      "name": "Huy K. Vo"
    },
    {
      "name": "Athanassios S. Fokas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3r14q1dv5n4qe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33886",
  "fulltext_url": null,
  "id": "3r14q1dv5n4qe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33886",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.33886",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3r14q1dv5n4qe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33886",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33886"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Well-posedness of the Burgers' equation on the half-line through the Cole-Hopf transformation",
  "title_text": "Well-posedness of the Burgers' equation on the half-line through the Cole-Hopf transformation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3r14q1dv5n4qe",
  "venue": "arXiv",
  "versions": []
}