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On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a kary interaction
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Kolokoltsov, V. N. (Vasiliĭ Nikitich). (2003) On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a kary interaction. Russian Journal of Mathematical Physics, Vol.10 (No.3). pp. 268295. ISSN 15556638

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Abstract
We deduce the kinetic equations describing the low density (and the large number of particles) limit of interacting particle systems with knary interaction of pure jump type supplemented by an underlying "free motion" being an arbitrary Feller process. The well posedness of the Cauchy problem together with the propagation of chaos property are proved for these kinetic equations under some reasonable assumptions. Particular cases of our general equations are given by (spatially nontrivial) Boltzmann and Smoluchovski equations with mollifier. Even for the classical binary models our analysis yield new results.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Statistics 
Library of Congress Subject Headings (LCSH):  Particles  Dynamics, Particles  Mathematical models 
Journal or Publication Title:  Russian Journal of Mathematical Physics 
Publisher:  M A I K Nauka  Interperiodica 
ISSN:  15556638 
Date:  2003 
Volume:  Vol.10 
Number:  No.3 
Page Range:  pp. 268295 
Status:  Peer Reviewed 
Publication Status:  Published 
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URI:  http://wrap.warwick.ac.uk/id/eprint/39374 
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