A formula for the post-gelation mass of a coagulation equation with a separable bilinear kernel

It is well known that solutions of the coagulation equation do not conserve mass if the coagulation kernel grows too rapidly. The phenomenon whereby conservation of mass breaks down in finite time is known as gelation and is physically interpreted as being caused by the appearance of an infinite “gel” or “superparticle”. In this paper we derive a formula for the post-gelation mass for the case of a separable bilinear kernel K ( λ , μ ) = θ ( λ ) θ ( μ ) , and investigate the asymptotic behaviour of the solution.