{
  "abstract": "We study a class of nonlinear drift--diffusion equations on $\\mathbb{R}^d$ with saturation-type mobilities, not necessarily concave. Under structural assumptions on the mobility and potentials, bounded-domain approximations and local Caccioppoli estimates yield weak solutions for all positive times and an $L^1$-contraction estimate. The same estimates provide local space--time compactness of time translates, whose subsequential limits are weak solutions. Under additional confinement assumptions, uniform mass-tail estimates yield a mass-preserving, free-energy dissipating $C_0$-semigroup of $L^1(\\mathbb{R}^d)$-contractions. In this confining setting, every trajectory converges strongly in $L^1(\\mathbb{R}^d)$ to a stationary state with the same mass, and the resulting time-limit operator is an $L^1$-contraction. Under the same assumptions, we also identify the unique global and $L^1$-local minimiser of the free energy at each fixed mass and prove that it is stationary under the semigroup.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40294",
  "author_total": 1,
  "authors": [
    {
      "name": "Alejandro Fernández-Jiménez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4179vz9ktsvsr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40294",
  "fulltext_url": null,
  "id": "4179vz9ktsvsr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40294",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40294",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4179vz9ktsvsr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40294",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40294"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Drift-diffusion equations with saturation on $\\mathbb{R}^d$",
  "title_text": "Drift-diffusion equations with saturation on ℝ^d",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4179vz9ktsvsr",
  "venue": "arXiv",
  "versions": []
}