On cross-diffusion systemsfor two populations subject to a common\n congestion effect

2017/09/26 by Maxime Laborde, Laborde, Maxime
Mathematics · #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1709.09109

Abstract

In this paper, we investigate the existence of solution for systems of\nFokker-Planck equations coupled through a common nonlinear congestion. Two\ndifferent kinds of congestion are considered: a porous media congestion or\n\soft congestion and the \hard congestion given by the\nconstraint \ρ₁+\ρ₂ leqslant 1. We show that these systems can be seen\nas gradient flows in a Wasserstein product space and then we obtain a\nconstructive method to prove the existence of solutions. Therefore it is\nnatural to apply it for numerical purposes and some numerical simulations are\nincluded.\n

Citations

• Polar factorization and monotone rearrangement of vector‐valued functions

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