{
  "abstract": "The exponential decay of weak solutions towards the constant steady state of general cross-diffusion systems in bounded domains with no-flux boundary conditions is investigated. The proof of quantitative decay rates is based on the relative entropy method and involves two parameters: the exponent determining the entropy density and the exponent in the entropy production integral. The key ingredient are novel convex Sobolev inequalities, which extend existing results in the literature to a broad range of values of the two parameters. These inequalities are established using convexity arguments and the Gagliardo-Nirenberg inequality.",
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  "article_type": null,
  "arxiv": "2609.27477",
  "author_total": 2,
  "authors": [
    {
      "name": "Noah Geltner"
    },
    {
      "name": "Ansgar Jüngel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5c09jqnd67wg7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27477",
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  "id": "5c09jqnd67wg7",
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  "landing_url": "https://arxiv.org/abs/2609.27477",
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      "2604|Nonlinear Partial Differential Equations"
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  "openalex": "W7214228128",
  "pdf_url": "https://arxiv.org/pdf/2609.27477",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5c09jqnd67wg7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27477",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27477"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
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  ],
  "title": "Large-time asymptotics for general cross-diffusion systems and novel convex Sobolev inequalities",
  "title_text": "Large-time asymptotics for general cross-diffusion systems and novel convex Sobolev inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/5c09jqnd67wg7",
  "venue": "arXiv",
  "versions": []
}