On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a k-ary interaction
Kolokoltsov, V. N. (Vasiliĭ Nikitich). (2003) On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a k-ary interaction. Russian Journal of Mathematical Physics, Vol.10 (No.3). pp. 268-295. ISSN 1555-6638
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We deduce the kinetic equations describing the low density (and the large
number of particles) limit of interacting particle systems with k-nary 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 non-trivial) 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|
|Page Range:||pp. 268-295|
[AG] E. DeAngelis, C.P. GrÄunfeld. The Cauchy Problem for the Generalized Boltzmann Equation with Dissipative Collisions. Appl. Math. Letters 14 (2001), 941-947.
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