The Discrete Unbounded Coagulation-Fragmentation Equation with Growth, Decay and Sedimentation

In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong. This paper extends several previous results both by considering a more general model and and also signnificantly weakening the assumptions. Theoretical conclusions are supported by numerical simulations.