{
  "abstract": "We study the slow motion of phase transition layers for a time-fractional Allen--Cahn equation with a Caputo time derivative of order $α\\in(0,1)$. We show that the fractional memory preserves the distinction between exponentially and algebraically slow dynamics associated with non-degenerate and degenerate potentials, respectively. In the non-degenerate case, layered solutions persist on an exponentially long time scale of order $\\exp(A/(α\\varepsilon))$, $A>0$, while in the degenerate case the corresponding algebraic time scale is modified by the factor $1/α$. Finally, we extend the analysis to nonlinear diffusion operators, considering both the $p$-Laplacian and a Perona--Malik type diffusion, showing that the same fractional slow-motion mechanism persists in these more general settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04208",
  "author_total": 3,
  "authors": [
    {
      "name": "Davide Cusseddu"
    },
    {
      "name": "Raffaele Folino"
    },
    {
      "name": "Luis Fernando López Ríos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7af59fsbd09km.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04208",
  "fulltext_url": null,
  "id": "7af59fsbd09km",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04208",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7220742318",
  "pdf_url": "https://arxiv.org/pdf/2610.04208",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7af59fsbd09km.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04208",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04208"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Slow motion for the time-fractional Allen-Cahn equation with linear and nonlinear diffusion",
  "title_text": "Slow motion for the time-fractional Allen-Cahn equation with linear and nonlinear diffusion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/7af59fsbd09km",
  "venue": "arXiv",
  "versions": []
}