We derive kinetic equations describing the low-density (and the large-number-of-particles) limit of interacting particle systems with k-ary interaction of pure jump type supplemented by an underlying "free motion" given by an arbitrary Feller process. The well-posedness of the Cauchy problem, as well as the propagation of the chaos property, is proved for these kinetic equations under some reasonable assumptions. The (spatially nontrivial) Boltzmann and Smoluchowski equations with a mollifier are special cases of our general equations. Our analysis produces new results even for the classical binary models.

Original languageEnglish
Pages (from-to)268-295
Number of pages28
JournalRussian Journal of Mathematical Physics
Volume10
Issue number3
StatePublished - 2003

    Research areas

  • interacting particles, k-ary interaction, measure-valued limits, kinetic equations, Boltzmann equation, coagulation and fragmentation, propagation of chaos, COAGULATION-FRAGMENTATION EQUATIONS, EXISTENCE, CONSERVATION, UNIQUENESS, BREAKAGE

ID: 86492574