{
  "abstract": "In this paper, we study a nonlinear Cauchy problem written in normal form \\begin{equation*} \\begin{cases} u_{tt} + A u+ Bu_t =D|u|^α, & t\\geq 0, x \\in \\mathbb{R}^n\\\\ u(0,x)=u_0(x),\\,u_t(0,x)=u_1(x). \\end{cases} \\end{equation*} Here~ $Af=\\mathscr{F}^{-1}(a(ξ)^2\\mathscr{F}f)$, with $a(ξ)$ homogeneous of order $k > 0$ under the assumption that the Hessian matrix of $a(ξ)$ is nonsingular, the operator $Bf=\\mathscr{F}^{-1}(b(ξ)\\mathscr{F}f)$ represents a weak dissipation, in the sense that $b(ξ) \\sim 1$ as $|ξ| \\to \\infty$ and %, in several models, $D=B$ but we also consider the case $Df=ν\\ast (-Δ)^δ(I-Δ)^{-δ}$, with $ν$ a bounded measure and $δ\\geq k/2$. We derive $L^p-L^q$ estimates of the linear solution operator to the considered model and we prove the transition from a Fujita-type exponent to a Strauss-type exponent for the global-in-time existence of small data solution for the corresponding nonlinear problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22616",
  "author_total": 2,
  "authors": [
    {
      "name": "Marcello D'Abbicco"
    },
    {
      "name": "Antonio Lagioia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/57fxcdtdn6mc0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22616",
  "fulltext_url": null,
  "id": "57fxcdtdn6mc0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22616",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7222954040",
  "pdf_url": "https://arxiv.org/pdf/2610.22616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/57fxcdtdn6mc0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22616"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the two critical exponents for a dispersive equation with weak dissipation",
  "title_text": "On the two critical exponents for a dispersive equation with weak dissipation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/57fxcdtdn6mc0",
  "venue": "arXiv",
  "versions": []
}