Singularities in the kinetics of coagulation processes

The authors consider a system of substances Ai reacting according to the following scheme: Ak+Al-RKl to k+l, (Rkl=Rlk>or=0). (The reaction is taken as irreversible.) They discuss the existence of global solutions of the kinetic equations derived for the concentrations. It is shown that one cannot expect the total number of monomers to remain constant. Rather, it can decrease as the result of the formation of infinite clusters (gelation). With this restriction, they obtain that a physically reasonable global solution exists if Rkl<or=rkrl and rk=o(k). It is further conjectured that no gelation will take place if rk=o( square root k). The case Rjk=(Aj+B)(Ak+B) is also solved explicitly and shown to exhibit gelation at t=1/A(A+B).