{
  "abstract": "We investigate the nonlinear stability of monotone traveling shock waves arising in the generalized Korteweg-de Vries-Burgers equation with a power-law flux, focusing on the cubic and quartic cases p=3 and p=4, respectively, in the presence of both dissipative and dispersive effects. Since shocks connecting distinct end states destroy the integrable structure of the equation, we introduce a slowly varying reference connection to establish global well-posedness for the Cauchy problem in an affine Sobolev space. A key ingredient in the stability analysis is to establish a new two-sided comparison estimate for the derivative of a monotone shock-wave profile. After a monotone coordinate transformation, this estimate allows the viscous dissipation to be compared with the natural vanishing weight arising in a shifted Poincare inequality. Together with an $L^\\infty$ bootstrap controlling the higher-order relative-flux terms, this yields a global $L^2$-contraction property modulo a time-dependent shift for sufficiently small $H^1$ perturbations in the admissible parameter regimes. We obtain exponential decay of the shock profile and show asymptotic convergence to the shifted shock in $L^q(\\R)$, $2<q\\leq \\infty$, with vanishing shift velocity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00595",
  "author_total": 4,
  "authors": [
    {
      "name": "Yi Du"
    },
    {
      "name": "Tao Yan"
    },
    {
      "name": "Yushu Zeng"
    },
    {
      "name": "Shihui Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ar3vby2ctsw4s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00595",
  "fulltext_url": null,
  "id": "ar3vby2ctsw4s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00595",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00595",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ar3vby2ctsw4s.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00595",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00595"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "L2-contraction and Asymptotic Stability of Monotone Shock Waves for Cubic and Quartic KdV-Burgers Equations",
  "title_text": "L2-contraction and Asymptotic Stability of Monotone Shock Waves for Cubic and Quartic KdV-Burgers Equations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/ar3vby2ctsw4s",
  "venue": "arXiv",
  "versions": []
}