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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. doi:10.1081/SAP-120028026 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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Volume: | Vol.22 | ||||
Number: | No.1 | ||||
Page Range: | pp. 113-141 | ||||
DOI: | 10.1081/SAP-120028026 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 |
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