{
  "abstract": "We consider a dynamic blocking problem: a fire, starting on a bounded open set $R_0\\subset\\mathbb R^2$, propagates in the plane with unit speed in all directions. To block it, a barrier can be constructed in real time, at speed $λ>0$. A long standing conjecture by the first author states that the fire can be entirely surrounded by the barrier, in finite time, if and only if $λ>2$. The present paper improves on earlier lower bounds. Namely, if $λ\\leq Λ=1.62621170228\\ldots $ we show that the fire cannot be blocked. We also prove that, if $λ\\leq 2$, the fire cannot be blocked by constructing a barrier which is a simple closed curve. More precisely, if the barrier does not contain purely delaying arcs, i.e.~arcs which are eventually surrounded by the fire on both sides, then for $λ<2$ the region burned by the fire at time $t>0$ has area $A(t)>(2-λ)t^2/4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36919",
  "author_total": 2,
  "authors": [
    {
      "name": "Alberto Bressan"
    },
    {
      "name": "Luca Talamini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/14ke3ryjh117n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36919",
  "fulltext_url": null,
  "id": "14ke3ryjh117n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36919",
  "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.OC"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7224076939",
  "pdf_url": "https://arxiv.org/pdf/2610.36919",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/14ke3ryjh117n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36919",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36919"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "On the Minimum Speed for a Fire Blocking Problem",
  "title_text": "On the Minimum Speed for a Fire Blocking Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/14ke3ryjh117n",
  "venue": "arXiv",
  "versions": []
}