Geodesic
Nonlinear Fokker--Planck--Kolmogorov equations in Hilbert spaces
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXVI. Representation theory, dynamical systems, combinatorial methods, Tome 437 (2015), pp. 184-206

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We study the Cauchy problem for nonlinear Fokker–Planck–Kolmogorov equations for probability measures on a Hilbert space, corresponding to stochastic partial differential equations. Sufficient conditions for the uniqueness of probability solutions for a cylindrical diffusion operator and for a possibly degenerate diffusion operator are given. A new general existence result is established without explicit growth restrictions on the coefficients. 
@article{ZNSL_2015_437_a8,
     author = {O. A. Manita},
     title = {Nonlinear {Fokker--Planck--Kolmogorov} equations in {Hilbert} spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {184--206},
     publisher = {mathdoc},
     volume = {437},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_437_a8/}
}
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O. A. Manita. Nonlinear Fokker--Planck--Kolmogorov equations in Hilbert spaces. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXVI. Representation theory, dynamical systems, combinatorial methods, Tome 437 (2015), pp. 184-206. http://geodesic.mathdoc.fr/item/ZNSL_2015_437_a8/