{
  "abstract": "In this paper, we consider the following reaction-diffusion system \\begin{equation*} \\begin{cases} u_t=Δu+F\\bigl(x,t,u,v,V(t)\\bigr), & (x,t)\\in\\Om\\times(0,T), v_t=Δv+G\\bigl(x,t,u,v,U(t)\\bigr), & (x,t)\\in\\Om\\times(0,T), \\mathcal B u=\\mathcal B v=0, & (x,t)\\in\\partial\\Om\\times(0,T), u(x,0)=u_0(x),\\quad v(x,0)=v_0(x), & x\\in\\Om, \\end{cases} \\end{equation*} where \\begin{equation*} U(t)=\\int_{\\Om}u(x,t)\\dd x,\\qquad V(t)=\\int_{\\Om}v(x,t)\\dd x, \\end{equation*} and the boundary operator $\\mathcal B$ is either \\[ \\mathcal B_D w=w \\qquad\\text{or}\\qquad \\mathcal B_N w=\\partial_νw, \\] $\\Om\\subset\\R^N$ be a bounded domain with sufficiently smooth boundary, $N\\ge 1$, and $ν$ is the outward unit normal on $\\partial\\Om$. Under certain conditions, we obtain the upper and lower bounds for the blowup time of the solution to the system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15367",
  "author_total": 4,
  "authors": [
    {
      "name": "Xin Zhao"
    },
    {
      "name": "Aynuer Ailatusi"
    },
    {
      "name": "Xianfa Song"
    },
    {
      "name": "Zeen Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7atqjwgnjf13k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15367",
  "fulltext_url": null,
  "id": "7atqjwgnjf13k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15367",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221751740",
  "pdf_url": "https://arxiv.org/pdf/2610.15367",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7atqjwgnjf13k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15367",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15367"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "pper and Lower Bounds for Blow-up Times in Coupled Reaction--Diffusion Systems with Nonlocal Sources",
  "title_text": "pper and Lower Bounds for Blow-up Times in Coupled Reaction--Diffusion Systems with Nonlocal Sources",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7atqjwgnjf13k",
  "venue": "arXiv",
  "versions": []
}