Long-time behavior of the cluster size distribution in joint coagulation processes

A kind of joint coagulation process which contains binary and tribasic collisions is considered, and an explicit expression of the cluster size distributions has been derived for the special coagulation kernels $R_2$(i,j)=ij and $R_3$(i,j,k)=ijk, subject to the monodisperse initial condition. The long-time behavior of the size distribution, $c_m$(t), has been discussed, and some interesting asymptotic properties of such coupled processes are revealed.