{
  "abstract": "We study the lifespan \\(T^*(\\varepsilon)\\) of classical solutions to the Cauchy problem for the one-dimensional quasilinear wave equation $u_{tt}-(c(u)^2u_x)_x=0$, with initial data of size $\\varepsilon>0$. We assume that $c'(θ)\\sim a|θ|^{p-2}$ as $θ\\to 0$, where \\(a>0\\) and \\(p>3\\) or $p=2$. We obtain explicit asymptotic formulas for $T^*(\\varepsilon)$ as $\\varepsilon\\downarrow0$. We treat both the case $ψ\\in L^1(\\mathbb R)$ and the case $ψ=ψ_1+\\Braket{x}^{-α}$, where \\(ψ_1\\in L^1(\\mathbb R)\\) and \\(0<α\\le1\\). Our results identify the dependence of the lifespan scale on the decay exponent, including the borderline case $α=1$. The proof combines Riccati equations along characteristics with a scaling argument inspired by Lindblad.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38353",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuusuke Sugiyama"
    },
    {
      "name": "Taro Yamanoi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ekts5y4d5x8a1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38353",
  "fulltext_url": null,
  "id": "ekts5y4d5x8a1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38353",
  "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/2610.38353",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ekts5y4d5x8a1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38353",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38353"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Asymptotic Formula of the Lifespan of Classical Solutions to 1D Quasilinear Wave Equations",
  "title_text": "Asymptotic Formula of the Lifespan of Classical Solutions to 1D Quasilinear Wave Equations",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/ekts5y4d5x8a1",
  "venue": "arXiv",
  "versions": []
}