The Discrete Coagulation-Fragmentation Equations: Existence, Uniqueness, and Density Conservation

The discrete coagulation-fragmentation equation describes the kinetics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters or fragment to form smaller ones. These models have many applications in pure and applied science ranging from cluster formation in galaxies to the kinetics of phase transformations in binary alloys. Our results relate to existence, uniqueness, density conservation and continuous dependence and they generalise the corresponding results in [ref. 2] for the Becker-Doring equations for which the processes are restricted to clusters gaining or shedding one particle. Examples are given which illustrate the role of the assumptions on the kinetic coefficients and show the rich set of analytic phenomena supported by the general discrete coagulation-fragmentation equations