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# On a General Kinetic Equation for Many-Particle Systems with Interaction, Fragmentation and Coagulation

V. P. Belavkin and V. N. Kolokol'tsov
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 459, No. 2031 (Mar. 8, 2003), pp. 727-748
Stable URL: http://www.jstor.org/stable/3560188
Page Count: 22
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## Abstract

We deduce the most general nonlinear kinetic equation that describes the low-density limit of general Feller processes for systems of random numbers of classical particles with interaction, collisions, fragmentation and coagulation. This is done by studying the limiting (as ε → 0) evolution of Feller processes on $\bigcup_{n = 0}^\infty X^n$ with X = Rd or X = Zd described by generators of the form ε-1k = 0K εk B(k), K ∈ N, where B(k) are the generators of k-nary interaction, whose general structure is also described in the paper.

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