2017/08/07 by Elisabetta Carlini, Francisco Silva, Carlini, Elisabetta +1 · 7 citations
Mathematics · Physics and Astronomy · #35Q84 #65N12 #65N75 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1708.02042
openalex publication_date 2017/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we consider the discretization of some nonlinear\nFokker-Planck-Kolmogorov equations. The scheme we propose preserves the\nnon-negativity of the solution, conserves the mass and, as the discretization\nparameters tend to zero, has limit measure-valued trajectories which are shown\nto solve the equation. The main assumptions to obtain a convergence result are\nthat the coefficients are continuous and satisfy a suitable linear growth\nproperty with respect to the space variable. In particular, we obtain a new\nproof of existence of solutions for such equations.\n We apply our results to several examples, including Mean Field Games systems\nand variations of the Hughes model for pedestrian dynamics.\n