New exactly solvable models of Smoluchowski's equations of coagulation

Abstract

The Smoluchowski equations of coagulation are solved analytically in two cases involving a finite cut-off of the system: the constant kernel set to zero for any j>N on the one hand, and the general three-particle case on the other. Both are seen to exhibit rather unusual large-time behaviour. The first model can be used to account for large particles precipitating out of a system and its behaviour is therefore of particular interest.