On the Extensions of the Mollified Boltzmann and Smoluchovski Equations to K-nary Interacting Particle Systems

Abstract. 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.