The generalized Vlasov kinetic equation. (English. Russian original) Zbl 1181.37006

Russ. Math. Surv. 63, No. 4, 691-726 (2008); translation from Usp. Mat. Nauk 63, No. 4, 93-130 (2008).
This article is concerned with the investigation of a generalized kinetic equation describing the evolution of the density of a probability measure. In the general case this is a non-linear integro-differential equation. The basic aim of this article is to attract the reader’s interest to the circle of problems related to weak convergence of solutions of non-linear integro-differential equations which are important for statistical mechanics and its applications. Also the author states several conjectures and unsolved problems.


37A60 Dynamical aspects of statistical mechanics
82B30 Statistical thermodynamics
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
82C35 Irreversible thermodynamics, including Onsager-Machlup theory
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