AI 中文总结
该研究将Fournier针对连续Smoluchowski凝并方程的确定性方法适配到离散OHS凝并系统，分析其解的凝胶化、质量守恒及正性，得到凝胶化时间界等关键结论。
AI 中文摘要
受Fournier[F2025]针对连续Smoluchowski凝并方程凝胶化的确定性方法启发，我们将其方法适配到离散Oort--Hulst--Safronov（OHS）凝并系统。我们证明，在凝并核的合适条件下，所有具有有限初始质量的解会在有限时间内损失质量，并给出凝胶化时间的显式界；还证明了临界对数情形下的凝胶化，给出质量守恒的充分条件；最后研究解的正性，证明任意正时间下，团簇尺寸具有正浓度当且仅当它至少不小于初始存在的最小团簇尺寸。
英文摘要
Motivated by the recent deterministic approach of Fournier~\cite{F2025} to gelation for the continuous Smoluchowski coagulation equation, we adapt his method to the discrete Oort--Hulst--Safronov (OHS) coagulation system. We show that under a suitable condition on the coagulation kernel, every solution with finite initial mass loses mass in finite time, and we give an explicit bound on the gelation time. We also prove gelation in the critical logarithmic case and provide a sufficient condition for mass conservation. Finally, we study the positivity of solutions and show that, for any positive time, a cluster size has positive concentration if and only if it is at least as large as the smallest cluster present initially.
Comments18 pages
