{
  "abstract": "We study the nonlinear stability of a composite wave consisting of a traveling wave and a rarefaction wave for a parabolic-hyperbolic system arising from chemotaxis. We prove that if the initial value is a small $H^1$-type perturbation of composite wave, then the system admits a global solution that converges toward the composite wave with an absolutely continuous shift. The proof combines the weighted relative-entropy mechanism for viscous shocks with the energy structure of rarefaction waves. A key ingredient is the inclusion of a rarefaction modulation factor in the weighted relative entropy; its derivatives combine with the terms generated by the rarefaction profile to produce a rarefaction dissipation. Moreover, the spatial separation of the two waves yields time-integrable interaction errors caused by the non-exact superposition. Since diffusion acts only on the density component, the full $H^1$ estimate is closed by exploiting the coupling structure of the system to recover the missing dissipation of the hyperbolic component.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23448",
  "author_total": 2,
  "authors": [
    {
      "name": "Sitong Liu"
    },
    {
      "name": "Jingyu Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9hg3fhs3xf0hj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23448",
  "fulltext_url": null,
  "id": "9hg3fhs3xf0hj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23448",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2611|Mathematical Biology Tumor Growth"
    ]
  ],
  "openalex": "W7214046813",
  "pdf_url": "https://arxiv.org/pdf/2609.23448",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9hg3fhs3xf0hj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23448",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23448"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Nonlinear stability of composite waves of traveling wave and rarefaction wave for a parabolic-hyperbolic system arising from chemotaxis",
  "title_text": "Nonlinear stability of composite waves of traveling wave and rarefaction wave for a parabolic-hyperbolic system arising from chemotaxis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9hg3fhs3xf0hj",
  "venue": "arXiv",
  "versions": []
}