Deterministic and Stochastic Becker-D\"oring equations: Past and Recent Mathematical Developments

TL;DR

This survey reviews recent mathematical advances in deterministic and stochastic Becker-D"oring equations, covering well-posedness, long-term dynamics, convergence, metastability, and connections to nucleation theory.

Contribution

It compiles recent results and open questions on the Becker-D"oring equations, emphasizing both deterministic and stochastic models and their complex behaviors.

Findings

Well-posedness established for both models

Convergence rates towards equilibrium analyzed

Insights into metastability and nucleation provided

Abstract

We present a survey on the results on a particular coagulation-fragmentation model given by the Becker-D\"oring equations. For both the deterministic and stochastic versions, we include well-posedness, long-time behavior, convergence rate towards equilibrium, coarsening and relation to transport equations, time-dependent properties, metastability and classical nucleation theory. All along this survey, we highlight recent results and open questions.