Nonlinear Fokker–Planck–Kolmogorov equations

V. I. Bogachev   ; S. V. Shaposhnikov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 79 (2024) no. 5, pp. 751-805

Résumé

This paper gives a survey of recent investigations on nonlinear Fokker–Planck–Kolmogorov equations of elliptic and parabolic types and contains a number of new results. We discuss in detail the problems of existence and uniqueness of solutions, various estimates of solutions, connections with linear equations, and the convergence of solutions of parabolic equations to stationary solutions. Bibliography: 116 items.

Détail

Keywords: Cauchy problem, Kantorovich metric.
Mots-clés : Fokker–Planck–Kolmogorov equation, elliptic equation, parabolic equation

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