Communications in Mathematical Sciences

Volume 2 (2004)

Supp. 1

Supplemental Issue 1

On a discrete Boltzmann-Smoluchowski equation with rates bounded in the velocity variables

Pages: 55 – 63



Nicolas Fournier (Institut Elie Cartan, Campus Scientifique, Vandoeuvre-lès-Nancy, France)

Stéphane Mischler (Département de Mathématiques, Université de Versailles-Saint-Quentin, Versailles, France)


Consider a spatially homogeneous infinite particle system in which coalescence and elastic collisions occur. The Boltzmann-Smoluchowski equation describes the evolution of the concentration $f(t, m, v)$ of particles of mass $m$ and velocity $v$ at time $t ≥ 0$. Using a stochastic version of this equation, we give an exact simulation scheme and we study the asymptotics of solutions for large times.


Boltzmann equations, Smoluchowski equations, Jump processes

2010 Mathematics Subject Classification

60J75, 82C40

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