{
  "abstract": "We study the decay rate for a quasilinear heat equation of the form $ \\dot u-\\Delta u = \\operatorname{div B}(\\nabla u)$. The term on the right-hand-side is interpreted as a nonlinear perturbation of the ordinary heat equation and we will prove an optimal decay rate for the solution. More precisely, under natural conditions on the operator $B \\colon \\R^d \\to \\R^d$, we show that for sufficiently regular initial data the solution decays as $t^{-d/4}$ and its gradient as $t^{-d/4 - 1/2}$ for large times, that is at the same rates as for the free heat equation. Furthermore, we prove that the difference between the quasilinear and the linear solution decays \\emph{strictly faster} than the solution of either equation generically does, that is that there is \\emph{asymptotic simplification}. All estimates are completely explicit and rely on variations of Fourier splitting techniques, originally introduced by Schonbek.",
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  "article_type": null,
  "arxiv": "2609.37662",
  "author_total": 3,
  "authors": [
    {
      "name": "Maryam Al Hajjar"
    },
    {
      "name": "Ioana Ciotir"
    },
    {
      "name": "Matthias Täufer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/66my405vs4wre.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37662",
  "fulltext_url": null,
  "id": "66my405vs4wre",
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  "landing_url": "https://hal.science/hal-05769211v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
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  "pdf_url": "https://hal.science/hal-05769211/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/66my405vs4wre.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
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      "url": "https://hal.science/hal-05769211v1"
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    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37662",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37662"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp decay rate and asymptotic simplification for a quasilinear heat equation",
  "title_text": "Sharp decay rate and asymptotic simplification for a quasilinear heat equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/66my405vs4wre",
  "venue": "HAL",
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}