Exact solutions to the coagulation equation

Abstract

Explicit post-gelation solutions are presented for Smoluchowski's coagulation equation with factorizable transition kernels Kij = sisj, when sk = kω (ω > 1/2) and sk = exp[α(k−1)] (α > 0). In such solutions the total mass of sol (finite clusters) is not conserved in time, as the sol is loosing mass to the gel (infinite cluster). For the kernels Kij = iμjν + jμiν (μ = 0, 1, ν general) Smoluchowski's equation can be solved sequentially in terms of a transformed time variable.