Non-linear Fokker-Planck-Kolmogorov equation as gradient flows on the space of probability measures
A talk in the CRC Seminar series by
Michael Röckner
| 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 $\mathbb R^d$ with a natural differential geometry. Our notion of gradient flow does not depend on any underlying metric structure such as the Wasserstein distance, but is derived from purely differential geometric principles. Moreover, we explicitly identify the associated energy functions and show that these are Lyapunov functions for the FPK solutions. Our main result covers classical and generalized porous media equations, where the latter have a generalized diffusivity function and a nonlinear transport-type first-order perturbation. Joint work with Marco Rehmeier. Zoom Meeting ID: [647 0432 3651] Passcode: [078107] $\href{https://uni-bielefeld.zoom.us/j/64704323651?pwd=OXhLSDluak9WTWkxU1RObmhGek9QQT09}{\textbf{Join Zoom Meeting}}$ Within the CRC this talk is associated to the project(s): A5 |