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 Probability Surveys > Vol. 14 (2017) open journal systems 

Coagulation and diffusion: A probabilistic perspective on the Smoluchowski PDE

Alan Michael Hammond, U.C. Berkeley

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.

AMS 2000 subject classifications: 60-02

Keywords: Smoluchowski PDE; kinetic limit; constant mean free path; Stosszahlansatz

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Hammond, Alan Michael, Coagulation and diffusion: A probabilistic perspective on the Smoluchowski PDE, Probability Surveys, 14, (2017), 205-288 (electronic). DOI: 10.1214/15-PS263.


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