Coagulation and diffusion: a probabilistic perspective on the Smoluchowski PDE

DOI10.1214/15-PS263zbMATH Open1384.82010arXiv1401.0829MaRDI QIDQ1683405

Publication date: 8 December 2017

Published in: Probability Surveys (Search for Journal in Brave)

Abstract: The Smoluchowski coagulation-diffusion PDE is a system of partial differential equations modelling the evolution in time of mass-bearing Brownian particles which are subject to short-range pairwise coagulation. This survey presents a fairly detailed exposition of the kinetic limit derivation of the Smoluchowski PDE from a microscopic model of many coagulating Brownian particles that was undertaken in [11]. It presents heuristic explanations of the form of the main theorem before discussing the proof, and presents key estimates in that proof using a novel probabilistic technique. The survey's principal aim is an exposition of this kinetic limit derivation, but it also contains an overview of several topics which either motivate or are motivated by this derivation.

Full work available at URL: https://arxiv.org/abs/1401.0829

zbMATH Keywords

diffusion Brownian motion Boltzmann equation coagulation Smoluchowski equation distributed particles

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Brownian motion (60J65) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Boltzmann equations (35Q20) Fokker-Planck equations (35Q84)