On coalescence equations and related models

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 probabilis- tic 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 conserva- tion, 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.