{
  "abstract": "We introduce a novel phase-field model approximating the Verigin problem with phase transition. For fixed interface thickness $\\varepsilon>0$, we construct weak solutions through a time-discrete variational scheme combining a Wasserstein minimizing-movement for the density with Schätzle's selection procedure for the phase field, which yields strong compactness and an almost-minimizing property. We then investigate the sharp-interface limit $\\varepsilon \\downarrow0$. For well-prepared initial data, we establish strong compactness of the densities and phase fields, and we prove convergence of the time-integrated diffuse interfacial energy to the perimeter. The limiting evolution is identified as a weak solution of the Verigin problem with phase transition, satisfying an optimal energy dissipation inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30412",
  "author_total": 2,
  "authors": [
    {
      "name": "Anna Kubin"
    },
    {
      "name": "Alice Marveggio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0j9hd733bbxk4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30412",
  "fulltext_url": null,
  "id": "0j9hd733bbxk4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30412",
  "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",
      "2505|Solidification and crystal growth phenomena"
    ]
  ],
  "openalex": "W7214586334",
  "pdf_url": "https://arxiv.org/pdf/2609.30412",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0j9hd733bbxk4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30412",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30412"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A phase-field model for the Verigin problem: weak solutions and sharp-interface limit",
  "title_text": "A phase-field model for the Verigin problem: weak solutions and sharp-interface limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/0j9hd733bbxk4",
  "venue": "arXiv",
  "versions": []
}