{
  "abstract": "We construct self-similar solutions to a nonlinear convection--diffusion equation posed on the whole Euclidean space, for a class of homogeneous initial data. The corresponding self-similar profiles solve a nonlinear elliptic equation on $\\mathbb{R}^N$. We obtain these profiles as limits of solutions to Dirichlet problems on bounded domains with truncated nonlinearities, using a priori estimates that are uniform with respect to both the domain size and the truncation level. Our approach is inspired by recent constructions of large self-similar solutions for the Navier--Stokes system. The convection--diffusion equation considered here shares some structural features with the Navier--Stokes equations, but its scalar parabolic nature allows us to exploit tools such as the maximum principle and thereby obtain a more direct construction of self-similar solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07259",
  "author_total": 4,
  "authors": [
    {
      "name": "Xiaoxin Zheng"
    },
    {
      "name": "Dominika Pilarczyk"
    },
    {
      "name": "Grzegorz Karch"
    },
    {
      "name": "Marco Cannone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cypfxsv6vza6x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07259",
  "fulltext_url": null,
  "id": "cypfxsv6vza6x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07259",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7220893650",
  "pdf_url": "https://arxiv.org/pdf/2610.07259",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cypfxsv6vza6x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07259",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07259"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Large self-similar solutions of a convection--diffusion equation",
  "title_text": "Large self-similar solutions of a convection--diffusion equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/cypfxsv6vza6x",
  "venue": "arXiv",
  "versions": []
}