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A rigorous derivation of Smoluchowski's equation in the moderate limit

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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. ISSN 1532-9356

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Official URL: http://dx.doi.org/10.1081/SAP-120028026

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

Identification Number:

10.1081/SAP-120028026

Status:

Peer Reviewed

Access rights to Published version:

Restricted or Subscription Access

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