{
  "abstract": "The present article investigates the well--posedness of a discrete coagulation--annihilation model originally introduced by E. Ben-Naim and P. Krapivsky in Physical Review E (1995). We first establish the existence of solutions for a broad class of coagulation and annihilation rates, including rates that may be unbounded. These results are obtained by combining uniform estimates with Helly's selection theorem and the Rellich--Kondrachov compact embedding theorem. Under appropriate structural assumptions on these rates, we further prove uniqueness and continuous dependence of solutions on the initial data, thereby establishing well--posedness of the model. Finally, for a specific class of coagulation and annihilation rates, we additionally study the differentiability of solutions and characterize their long--time asymptotic behaviour. These results provide a rigorous mathematical framework for the analysis of the model and contribute to a deeper understanding of its well--posedness, regularity, and long-time dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18618",
  "author_total": 3,
  "authors": [
    {
      "name": "Ikjot Kaur"
    },
    {
      "name": "Saroj Si"
    },
    {
      "name": "Ankik Kumar Giri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23qbes24d0gsf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18618",
  "fulltext_url": null,
  "id": "23qbes24d0gsf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18618",
  "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|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7213523382",
  "pdf_url": "https://arxiv.org/pdf/2609.18618",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23qbes24d0gsf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18618",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18618"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the well-posedness and long-time dynamics of a discrete coagulation--annihilation system",
  "title_text": "On the well-posedness and long-time dynamics of a discrete coagulation--annihilation system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/23qbes24d0gsf",
  "venue": "arXiv",
  "versions": []
}