Deterministic and stochastic becker-döring equations: Past and recent mathematical developments

Abstract

Becker and Dörimy introduced their equations in 1935 to describes nucleation in supersaturated vapors. Since then, these equations have been popularized to a wide range of applications and Slemrod in 2000 said they “provide perhaps the simplest kinetic model to describe […] phase transitions”. In this survey we attempt to give an overview of the results obtained on these equations in the parts decades until today. Particularly we gathered results on both deterministic and stochastic versions of the Becker-Dörimy equations.