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.
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Marco Bonacini, Barbara Niethammer, Juan J.L. Velázquez, Solutions with peaks for a coagulation-fragmentation equation. Part II: Aggregation in peaks. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 3, pp. 601–646DOI 10.1016/J.ANIHPC.2020.08.007