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arXiv · 1708.02042

On the discretization of some nonlinear Fokker-Planck-Kolmogorov equations and applications

Elisabetta Carlini·Francisco J. Silva
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Abstract

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.

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Elisabetta Carlini, Francisco J. Silva. 2017-08-07. On the discretization of some nonlinear Fokker-Planck-Kolmogorov equations and applications. https://arxiv.org/abs/1708.02042

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