Boltzmann-grad limit for a particle system in continuum
The authors derive the discrete Boltzmann equation as the kinetic limit of a one-dimensional particle system with particles travelling with fixed velocity between stochastic collisions. The proof is based on an entropy bound, from which there follows, that there are only finitely many collisions per unit time. A similar model was studied by the first author [Probab. Theory Relat. Fields 104, No. 1, 97-146 (1996; Zbl 0838.60085)], in which particles perform a random walk between stochastic collisions.
scientific article; zbMATH DE number 1100522