Kozlov, V. V. 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. Reviewer: Tatiana Mamedova (Saransk) Cited in 42 Documents 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 Keywords:kinetic equation; dynamical systems; integro-differential equation PDFBibTeX XMLCite \textit{V. V. Kozlov}, Russ. Math. Surv. 63, No. 4, 691--726 (2008; Zbl 1181.37006); translation from Usp. Mat. Nauk 63, No. 4, 93--130 (2008) Full Text: DOI