Time asymptotics for a Becker–Döring-type model of aggregation with collisional fragmentation

The large time behaviour of solutions to a discrete model of cluster coagulation with collisional breakage is studied. The interactions between clusters taken into account are restricted to the collisions of monoclusters with i-clusters, i≥1, resulting in either an (i+1)-cluster (coalescence) or an (i−1)-cluster and two monoclusters (fragmentation)—an assumption reminiscent of the Becker–Döring model. In comparison to the Becker–Döring model, the set of steady states exhibits a more complicated structure and we show the convergence of solutions to steady states in both the coagulation-dominated and the fragmentation-dominated cases.