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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.

MSC:
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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