Strongly Differentiable Solutions of the Discrete Coagulation-Fragmentation Equation

We examine an infinite system of ordinary differential equations that models the coagulation and fragmentation of clusters. In contrast to previous investigations, we allow multiple fragmentation to occur and our analysis does not involve finite-dimensional truncations of the system. Instead, we treat the problem as an infinite-dimensional differential equation, posed in an appropriate Banach space, and apply perturbation results from the theory of strongly continuous semigroups of operators. The existence and uniqueness of physically meaningful solutions are established under minimal restrictions on the fragmentation rates, but with the coagulation rates assumed to be uniformly bounded. PACS (2008): 82.30.Nr, 02.30.Hq, 02.30.Tb, 04.20.Ex