## Nonlinear Fokker-Planck-Kolmogorov Equations as Gradient Flows on the Space of Probability Measures

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#### ABSTRACT

We propose a general method to identify nonlinear Fokker-Planck-Kolmogorov equations (FPK equations) as gradient flows on the space of Borel probability measures on

Keywords: Gradient flow, nonlinear Fokker-Planck equations, generalized porous media equation, differential geometry, Barenblatt solution

2020 MSC: 35Q84 (Fokker-Planck eq.), 35K55 (nonl. Parab. Eq.), 76S05 (flows in porous media), 58B20 (Riem. Geometry on infin. Dim. Spaces), 37B35 (gradient-like behavior), 35B40 (asympt. Behavior of sol. To PDE)

Joint work with:

Marco Rehmeier, Faculty of Mathematics, Bielefeld University, Germany