On coalescence equations and related models

Abstract

Summary: The Smoluchowski coalescence equation is a mean-field model for the growth of particles by successive mergers, and has been recently studied by deterministic and probabilistic methods. The present review article focuses on the deterministic approach and attempts to survey the currently available results on the questions of existence, uniqueness, mass conservation, gelation and large time behaviour, while sketching the needed mathematical tools. When fragmentation is also taken into account and a detailed balance condition is assumed, recent techniques used to investigate the trend to equilibrium are outlined. \par The bibliography contains 116 references.