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JOURNALS // Uspekhi Matematicheskikh Nauk // Archive

Uspekhi Mat. Nauk, 2024 Volume 79, Issue 5(479), Pages 3–60 (Mi rm10202)

Nonlinear Fokker–Planck–Kolmogorov equations

V. I. Bogachevab, S. V. Shaposhnikovab

a Lomonosov Moscow State University
b National Research University "Higher School of Economics"

Abstract: 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.

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

UDC: 517.5+519.2

MSC: Primary 35G20, 35Q84, 35R06; Secondary 35Q83

Received: 06.08.2024

DOI: 10.4213/rm10202


 English version:
Russian Mathematical Surveys, 2024, 79:5, 751–805

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© Steklov Math. Inst. of RAS, 2025