Grosskinsky, Stefan, Klingenberg, C. and Oelschläger, K. (2006) A rigorous derivation of Smoluchowski's equation in the moderate limit. Stochastic Analysis and Applications, Vol.22 (No.1). pp. 113-141. doi:10.1081/SAP-120028026

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Abstract

Smoluchowski’s equation is a macroscopic description of a many particle system
with coagulation and shattering interactions. We give a microscopic model of
the system from which we derive this equation rigorously. Provided the existence
of a unique and sufficiently regular solution of Smoluchowski’s equation, we prove
the law of large numbers for the empirical processes. In contrast to previous derivations
we assume a moderate scaling of the particle interaction, enabling us to estimate
the critical fluctuation terms by using martingale inequalities. This approach
can be justified in the regime of high temperatures and particle densities, which is of
special interest in astrophysical studies and where previous derivations do not apply.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Particles -- Mathematical models, Reaction-diffusion equations
Journal or Publication Title:	Stochastic Analysis and Applications
Publisher:	Taylor & Francis Inc.
ISSN:	1532-9356
Official Date:	2006
Dates:	Date Event 2006 Published
Volume:	Vol.22
Number:	No.1
Page Range:	pp. 113-141
Identifier:	10.1081/SAP-120028026
Status:	Peer Reviewed
Access rights to Published version:	Restricted or Subscription Access

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