{"ID":22938772,"CreatedAt":"2026-09-17T01:37:05.451791504Z","UpdatedAt":"2026-09-17T01:37:05.451791504Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18618","arxiv_id":"2609.18618","title":"On the well-posedness and long-time dynamics of a discrete coagulation--annihilation system","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.","short_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 unbound...","url_abs":"https://arxiv.org/abs/2609.18618","url_pdf":"https://arxiv.org/pdf/2609.18618v1","authors":"[\"Ikjot Kaur\",\"Saroj Si\",\"Ankik Kumar Giri\"]","published":"2026-09-16T13:09:09Z","proceeding":"math.AP","tasks":"[\"math.AP\"]","methods":"[]","has_code":false}