The Discrete Generalized Exchange‐Driven System

ABSTRACT We study a discrete model for generalized exchange‐driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange‐driven growth system and the coagulation‐fragmentation system with binary fragmentation. Under reasonable general condition on the rate coefficients we establish the existence of admissible solutions, meaning solutions that are obtained as appropriate limit of solutions to a finite‐dimensional truncation of the infinite‐dimensional ODE. For these solutions, we prove that, in the class of models, we call isolated both the total number of particles and the total mass are conserved, whereas in those models, we can non‐isolated only the mass is conserved. Additionally, under more restrictive growth conditions for the rate equations, we obtain uniqueness of solutions to the initial value problems.