{
  "abstract": "To better understand how populations respond to dynamic external pressure, we propose a new diffusion model in the moving half-line {z ≥ b(t)}, where the boundary position b(t) is a given nondecreasing function of time. A Robin boundary condition is imposed at z = b(t) to prevent individuals from leaving the domain, so that the shifting boundary acts as an impermeable wall—a \"piston\"—that sweeps the individuals it encounters. Our analysis focuses on the cases where b(t) ∼ ct^β with β ∈ [0, 1]. We prove quantitative convergence results characterized by attraction toward self-similar profiles, based on entropy techniques and Duhamel's principle. When β goes through the critical value 1/2, the shape of the self-similar asymptotic profile switches from Gaussian to exponential. In particular, this profile turns out to be stationary when β = 1, reflecting a delicate balance between diffusion and advection induced by the moving boundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2505.03304",
  "author_total": 2,
  "authors": [
    {
      "name": "Samuel Tréton"
    },
    {
      "name": "Mingmin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e36gg4rwf7wrn.bib",
  "cited_by": 0,
  "doi": "10.1137/25m1757435",
  "fulltext_url": null,
  "id": "e36gg4rwf7wrn",
  "issns": [
    "0036-1399",
    "1095-712X"
  ],
  "landing_url": "https://hal.science/hal-05054852v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W4415144329",
  "pdf_url": "https://hal.science/hal-05054852/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": "Society for Industrial and Applied Mathematics",
  "ris": "https://research.draconitic.com/paper/e36gg4rwf7wrn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:35Z",
      "native_id": "hal-05054852",
      "source": "hal",
      "url": "https://hal.science/hal-05054852v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A piston to counteract diffusion: The influence of an inward-shifting boundary on the heat equation in half-space",
  "title_text": "A piston to counteract diffusion: The influence of an inward-shifting boundary on the heat equation in half-space",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:35Z",
  "url": "https://research.draconitic.com/paper/e36gg4rwf7wrn",
  "venue": "SIAM Journal on Applied Mathematics",
  "versions": []
}