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On the discretization of some nonlinear Fokker-Planck-Kolmogorov equations and applications by Carlini, Elisabetta; Silva, Francisco J. is a scholarly article available to read on EtoBox.

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In this work, we consider the discretization of some nonlinear Fokker-Planck-Kolmogorov equations. The scheme we propose preserves the non-negativity of the solution, conserves the mass and, as the discretization parameters tend to zero, has limit measure-valued trajectories which are shown to solve the equation. The main assumptions to obtain a convergence result are that the coefficients are continuous and satisfy a suitable linear growth property with respect to the space variable. In particular, we obtain a new proof of existence of solutions for such equations. We apply our results to several examples, including Mean Field Games systems and variations of the Hughes model for pedestrian dynamics.

Author

Carlini, Elisabetta; Silva, Francisco J.

Published

2017

Language

EN