{
  "abstract": "We consider a generalisation of the probabilistic reformulation of the supercooled Stefan problem from arXiv:1902.05174 allowing for non-integrable initial data. From an application of Ito's formula, we obtain a relationship between the Laplace transform of the initial data and a transform of the solution, together with its possibly discontinuous free boundary. Using this relationship we give a sharp existence result for global solutions, we extend previous results on the uniqueness of solutions, and we determine the asymptotic behaviour of solutions for a certain class of initial data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24297",
  "author_total": 2,
  "authors": [
    {
      "name": "Thomas Blore"
    },
    {
      "name": "Ben Hambly"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dwszn0307vwvs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24297",
  "fulltext_url": null,
  "id": "dwszn0307vwvs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24297",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.24297",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dwszn0307vwvs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24297",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24297"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A transform approach to the supercooled Stefan problem",
  "title_text": "A transform approach to the supercooled Stefan problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/dwszn0307vwvs",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1214/26-ecp814",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}