{
  "abstract": "We study a vanishing-regularization limit for a degenerate cross-diffusion system on the simplex when the active boundary stratum of a smooth reference solution may change in space and time. The mobility $M(u)=\\operatorname{diag}u-u\\otimes u$ loses rank when a component vanishes, so a fixed relative entropy or an unweighted two-point gradient estimate cannot remain uniformly coercive across moving faces. We introduce a geometric-relative framework that separates the single emerging normal direction from the active tangential subsystem. Its ingredients are a global resolvent geodesic distance, a boundary-oriented rank-one perspective correction, an intrinsic Schur-normal De Giorgi alternative, a mean-free tangential iteration with temporal-flux control, and a terminal coupled Schur compactness argument. These mechanisms yield a non-circular first-exit theorem for smooth approximations and then pass to admissibly approximable entropy weak solutions. If the strong solution stays a fixed distance from the codimension-two skeleton and its vanishing components satisfy $|\\nabla v_i|\\lesssim v_i^α$ and $|\\{0<v_i<r\\}|\\lesssim r^σ$, then the augmented relative energy is bounded by $ρ_λ=λ^{2α+σ}$ if $2α+σ<2$, $ρ_λ=λ^2|\\logλ|$ if $2α+σ=2$, and $ρ_λ=λ^2$ if $2α+σ>2$. For a hypersurface contact $v_i\\asymp d^p$, $p\\ge2$, this gives $ρ_λ=O(λ^{2-1/p})$ and $\\|u^λ-v\\|_{L^\\infty(0,T;L^2)}=O(λ^{1-1/(2p)})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22079",
  "author_total": 3,
  "authors": [
    {
      "name": "E. Yu. Shchetinin"
    },
    {
      "name": "A. A. Shevchuk"
    },
    {
      "name": "S. I. Salpagarov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/96h7bc0h35d9p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22079",
  "fulltext_url": null,
  "id": "96h7bc0h35d9p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22079",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7222485101",
  "pdf_url": "https://arxiv.org/pdf/2610.22079",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/96h7bc0h35d9p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22079",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22079"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative vanishing-regularization limits for degenerate cross-diffusion with changing boundary strata",
  "title_text": "Quantitative vanishing-regularization limits for degenerate cross-diffusion with changing boundary strata",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/96h7bc0h35d9p",
  "venue": "arXiv",
  "versions": []
}