{
  "abstract": "This paper investigates the global dynamics of a doubly degenerate nutrient-taxis system with indirect consumption: \\begin{equation*} \\left\\{ \\begin{aligned} &u_{t}=\\nabla \\cdot (uv\\nabla u)-\\nabla \\cdot (u^{2}v\\nabla v)+\\ell vw,&x\\in Ω,\\, t>0,\\\\ & v_{t}=Δv-vw,&x\\in Ω,\\, t>0,\\\\ &w_t=Δw-w+u,&x\\inΩ,t>0 \\end{aligned} \\right. \\end{equation*} posed on a smooth bounded domain $Ω\\subset\\mathbb{R}^{3}$ with no-flux boundary conditions. It is shown that for suitably regular initial data $(u_0,v_0,w_0)$, the associated initial-boundary value problem admits a global weak solution. Furthermore, in an appropriate topological setting, this solution converges to an equilibrium $(u_\\infty, 0,w_\\infty)$ as $t\\rightarrow \\infty$. Notably, when $u_0$ is nonconstant and the mass of $v_0$ is sufficiently small, the limiting profiles $u_{\\infty}$ and $w_{\\infty}$ are are spatially nonhomogeneous, capturing emergent patterning in nutrient-depleted environments. A cornerstone of our analysis is the introduction of novel functional inequalities, which provide estimates from below for the integral $\\int_Ωu^{k}v|\\nabla u|^2$ with some $k>-1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02607",
  "author_total": 4,
  "authors": [
    {
      "name": "Ai Huang"
    },
    {
      "name": "Xiangmao De-ji"
    },
    {
      "name": "Jing Li"
    },
    {
      "name": "Yifu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/24qynpthj0y82.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02607",
  "fulltext_url": null,
  "id": "24qynpthj0y82",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02607",
  "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",
      "2611|Mathematical Biology Tumor Growth"
    ]
  ],
  "openalex": "W7207589293",
  "pdf_url": "https://arxiv.org/pdf/2609.02607",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/24qynpthj0y82.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02607",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02607"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spatial inhomogeneity for a three-dimensional doubly degenerate nutrient system with indirect consumption",
  "title_text": "Spatial inhomogeneity for a three-dimensional doubly degenerate nutrient system with indirect consumption",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/24qynpthj0y82",
  "venue": "arXiv",
  "versions": []
}