{
  "abstract": "We study the uniform stability of composite waves consisting of a degenerate Oleinik shock and a rarefaction wave for scalar viscous conservation laws. We consider cubic-type fluxes and arbitrarily large $L^2$ initial perturbations of the composite wave within the $H^1$ strong-solution class. We obtain a uniform $L^2$ estimate for such large perturbations. In particular, the estimate implies the contraction of a degenerate Oleinik shock, up to a dynamical shift. As a further consequence, the uniformity with respect to viscosity implies that the associated self-similar solution, composed of the degenerate shock and rarefaction, is stable in the class of inviscid limits. The main analytical difficulty is that the standard weighted Poincaré inequality underlying the $a$-contraction method fails to yield the required coercivity at the linear level. We overcome this obstruction by establishing a new degenerate Hardy--Poincaré inequality adapted to the degenerate structure of the shock profile. Combined with an exact nonlinear decomposition, this linear inequality yields a strict coercivity estimate that controls the quadratic energy together with the higher-order nonlinear terms, without any smallness assumption on the perturbation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26351",
  "author_total": 3,
  "authors": [
    {
      "name": "Moon-Jin Kang"
    },
    {
      "name": "Bongsuk Kwon"
    },
    {
      "name": "Wanyong Shim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4pgsc9t3b9qp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26351",
  "fulltext_url": null,
  "id": "d4pgsc9t3b9qp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26351",
  "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|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214103283",
  "pdf_url": "https://arxiv.org/pdf/2609.26351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4pgsc9t3b9qp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniform Stability of degenerate Oleinik shock and rarefaction waves under large perturbations",
  "title_text": "Uniform Stability of degenerate Oleinik shock and rarefaction waves under large perturbations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/d4pgsc9t3b9qp",
  "venue": "arXiv",
  "versions": []
}