{
  "abstract": "We show global existence of weak solutions to the following system of partial differential equations with nonlinear diffusion in both equations and anisotropic signal production \\begin{equation} \\begin{cases} u_t=\\nabla\\cdot((u+1)^{m_1-1}\\nabla u)-\\nabla\\cdot(u\\nabla v), \\\\ v_t=\\nabla\\cdot((v+1)^{m_2-1}\\nabla v)+\\nabla\\cdot(u\\nabla v)-v+u, \\end{cases} \\end{equation} in a smooth bounded domain $Ω\\subseteq\\mathbb{R}^n$, $n\\in\\mathbb{N}$ with nonnegative initial data and homogenuous Neumann boundary conditions. Moreover, we show boundedness of $u$ in $L^\\infty((0,\\infty);\\:L^{m_1}(Ω))$ and $v$ in $L^\\infty(Ω\\times(0,\\infty))$. The strategy will be to show global existence and boundedness of classical solutions $(u_\\varepsilon,v_\\varepsilon)$ to the approximating system \\begin{equation} \\begin{cases} u_{\\varepsilon t}=\\nabla\\cdot((u_\\varepsilon+1)^{m_1-1}\\nabla u_\\varepsilon) -\\nabla\\cdot(\\frac{u_\\varepsilon\\nabla v_\\varepsilon}{1+\\varepsilon\\vert\\nabla v_\\varepsilon\\vert}), \\\\ v_{\\varepsilon t}=\\nabla\\cdot((v_\\varepsilon+1)^{m_2-1}\\nabla v_\\varepsilon)+\\nabla\\cdot(u_\\varepsilon\\nabla v_\\varepsilon)-v_\\varepsilon+u_\\varepsilon. \\end{cases} \\end{equation} Passing to the limit $\\varepsilon\\searrow 0$, we obtain convergence of weak solutions of the second to weak solutions of the first system. One of the main challenges lie in the proof of weak convergence of $\\frac{\\nabla v_\\varepsilon}{1+\\varepsilon\\vert\\nabla v_\\varepsilon\\vert}$ to $\\nabla v$ in $L^2(Ω\\times(0,T))$ for $T\\in(0,\\infty)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11462",
  "author_total": 1,
  "authors": [
    {
      "name": "Max Hegenbart"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4wgrtm3rrzys4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11462",
  "fulltext_url": null,
  "id": "4wgrtm3rrzys4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11462",
  "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|Mathematical Biology Tumor Growth"
    ]
  ],
  "openalex": "W7221148136",
  "pdf_url": "https://arxiv.org/pdf/2610.11462",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4wgrtm3rrzys4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11462",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11462"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global existence of weak solutions in a Keller-Segel system with local anisotropy and nonlinear diffusion",
  "title_text": "Global existence of weak solutions in a Keller-Segel system with local anisotropy and nonlinear diffusion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/4wgrtm3rrzys4",
  "venue": "arXiv",
  "versions": []
}