Existence and properties of post-gel solutions for the kinetic equations of coagulation

The kinetic equations of coagulation with kernels R ij are studied for both factorisable (R ij =r i r j ) and diagonal (R ij =A i delta ij ) kernels. It is rigorously shown that they allow solutions of the type c j (t)=a j /t for suitably chosen a j . These solutions are further shown to have finite mass if R jj approximately j d for d>1. The asymptotic behaviour of the a j is also studied and found to agree with numerous previous findings.