The aim of this two-part paper is to investigate the stability properties of a special class of solutions to a coagulation-fragmentation equation. We assume that the coagulation kernel is close to the diagonal kernel, and that the fragmentation kernel is diagonal. In a companion paper we constructed a two-parameter family of stationary solutions concentrated in Dirac masses, and we carefully studied the asymptotic decay of the tails of these solutions, showing that this behaviour is stable. In this paper we prove that for initial data which are sufficiently concentrated, the corresponding solutions approach one of these stationary solutions for large times.

中文翻译：

---

带有峰顶的凝结-破碎方程解。第二部分：高峰中的聚集

这篇分为两部分的文章的目的是研究凝结-破碎方程的一类特殊解决方案的稳定性。我们假设凝结核接近对角核，而碎裂核是对角线。在同伴论文中，我们构造了集中在Dirac质量中的两参数平稳解族，我们仔细研究了这些解的尾部的渐近衰减，表明此行为是稳定的。在本文中，我们证明了对于足够集中的初始数据，相应的解决方案在很长时间内都接近这些固定解之一。