{
  "abstract": "The large time dynamics of the weakly damped non-autonomous Korteweg-de Vries-Burgers equation \\begin{equation*} u_t + u_{xxx}+ uu_x + λu - μu_{xx} = g(x,t) \\end{equation*} in the phase space $L^2(\\mathbb R)$ is investigated. Due to the low regularity of the initial data, the framework of Bourgain spaces is employed. We first obtain the existence of a unique pullback attractor $\\{\\mathcal A_μ(t)\\}_{t\\in\\mathbb R}$ in $L^2(\\mathbb R)$ for each $μ\\ge 0$. Then we show an optimal asymptotic smoothing effect of the equation, namely the pullback attractor is compact in $H^3(\\mathbb R)$. These results are proved by using an energy equation method, splitting solutions into parts with low and high frequencies and exploiting a dispersive regularization. Furthermore, the attractors are shown to be upper semicontinuous as $μ\\to 0$ and have finite fractal dimensions in $H^1(\\mathbb R)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03905",
  "author_total": 4,
  "authors": [
    {
      "name": "Cung The Anh"
    },
    {
      "name": "Nesibe Ayhan"
    },
    {
      "name": "Bao Quoc Tang"
    },
    {
      "name": "Ingo Witt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4amj6m11900cv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03905",
  "fulltext_url": null,
  "id": "4amj6m11900cv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03905",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03905",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4amj6m11900cv.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03905",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03905"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Large time dynamics for non-autonomous weakly damped KdV-Burgers equations on the real line",
  "title_text": "Large time dynamics for non-autonomous weakly damped KdV-Burgers equations on the real line",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/4amj6m11900cv",
  "venue": "arXiv",
  "versions": []
}