The Smoluchowski coagulation equations with continuous injection

We study a system of equations which models the formation of clusters by coagulation, with particles of unit size being injected at a time-dependent rate. We observe that the criteria under which gelation occurs are the same as for the constant mass and constant monomer cases, which have been studied previously. We identify a variety of types of behaviour in the large-time limit, depending on the coagulation kernel and on the rate at which monomer is introduced into the system. The results are obtained by means of exact (generating function) techniques, matched asymptotic expansions and numerical simulations.