Nonlinear Fokker–Planck–Kolmogorov Equations for Measures
Existence and uniqueness of solutions of the Cauchy problem for nonlinear Fokker–Planck–Kolmogorov equations for measures are investigated. We consider the difficult case when the diffusion matrix depends on the solution. Moreover we give a short survey of the known results connected with these problems.
KeywordsNonlinear Fokker–Planck–Kolmogorov equation McKean–Vlasov equation Existence and uniqueness of solutions to the Cauchy problem for nonlinear parabolic equations
AMS subject classification.35K55 35Q84 35Q83
The author is grateful to Prof. V.I. Bogachev and Prof. M. Röckner for fruitful discussions and valuable remarks. The work was supported by the President Grant MD-207.2017.1, the RFBR grant 17-01-00622, the Simons Foundation, and the SFB 1283 at Bielefeld University.
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