Convergence to Stationary Measures in Nonlinear Fokker–Planck–Kolmogorov Equations¹

V. I. Bogachev^a^,^b^,^c^,*, M. Röckner^d, and S. V. Shaposhnikov ^a^,^b^,^c

^aDepartment of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia

^bNational Research University Higher School of Economics, Moscow, Russia

^cOrthodox S.-Tikhon’s Humanitarian University, Moscow, Russia

^dFaculty of Mathematics, Bielefeld University, Bielefeld, Germany

Correspondence to: *e-mail: vibogach@mail.ru

¹The article was translated by the authors.

Received 18 April, 2018

Abstract—The convergence of solutions of nonlinear Fokker–Planck–Kolmogorov equations to stationary solutions is studied. Broad sufficient conditions for convergence in variation with an exponential bound are obtained.

DOI: 10.1134/S1064562418060169

Convergence to Stationary Measures in Nonlinear Fokker–Planck–Kolmogorov Equations1

Convergence to Stationary Measures in Nonlinear Fokker–Planck–Kolmogorov Equations¹