{
  "abstract": "In this paper, we investigate finite-time blow-up solutions for distributed delay differential equations incorporating memory effects with a specific gamma distribution kernel. Focusing on typical nonlinear terms that cause finite-time singularities in ordinary differential equations (ODEs), we examine how memory effects change the existence, rate, and qualitative properties of blow-up. By comparing these behaviors with those of the corresponding non-delayed and memory-free ODEs, we show that time delay originating from memory not only essentially induces finite-time blow-up (``memory-induced blow-up''), but also drastically alters the blow-up profile, such as accelerating algebraic blow-up rates or driving a qualitative transition from ODE quenching to logarithmic blow-up. Furthermore, by incorporating a self-inhibitory term, we reveal a threshold phenomenon in the phase space that governs the occurrence and non-occurrence of blow-up depending on the initial conditions and parameters. These results are established by reducing the system to a two-dimensional ODE via the linear chain trick, and analyzing the dynamics at infinity using Poincaré-type compactification, blow-up techniques, and the center manifold theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15470",
  "author_total": 1,
  "authors": [
    {
      "name": "Yu Ichida"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dgxygh14gxf6m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15470",
  "fulltext_url": null,
  "id": "dgxygh14gxf6m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15470",
  "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.DS"
    ],
    [
      "openalex",
      "2604|Nonlinear Differential Equations Analysis"
    ]
  ],
  "openalex": "W7213317805",
  "pdf_url": "https://arxiv.org/pdf/2609.15470",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dgxygh14gxf6m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15470",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15470"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Memory-induced blow-up solutions and their dynamical transitions in distributed delay differential equations",
  "title_text": "Memory-induced blow-up solutions and their dynamical transitions in distributed delay differential equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/dgxygh14gxf6m",
  "venue": "arXiv",
  "versions": []
}