On a discrete Boltzmann-Smoluchowski equation with rates bounded in the velocity variables
Résumé
In this paper, the authors introduce a model of coagulation for macroscopic particles described by their mass and velocity. This model is related to the theory of sprays. Under an assumption of boundedness on the kernel of coagulation (in the space of velocities), they are able to prove that the equation of coagulation is related to a stochastic differential equation. They show that this stochastic equation admits a solution (which can be described in an explicit way). Then, some qualitative properties of the solution are presented: it admits a density, and the mass tends to infinity almost surely.