Large number asymptotics for two--component systems with self--consistent coupling

Abstract

{We shall consider the large number asymptotics of particle models for partial differential equations describing two component mixtures with simplest kind of self--consistent couplings. We shall recall in particular two examples related to different classes of models, the first one having both particle-like components and the second one having only one particle-like component (the other being described as a fluid); for these examples, different techniques on the probabilistic and analytic point of view are to be used to rigorously prove the convergence to a limit of the self-consistent terms in a "mean-field"-like asymptotics. The two models were analysed resp. in [C.Bernardin, V.Ricci: Kinetic and Related Models, Vol. 4, N. 3, pp. 633--668 (2011)] and [L.Desvillettes, F. Golse, V.Ricci: Derivation of a homogenized two-temperature model from the heat equation preprint hal--00827912, arXiv:1305.6920, 2013].