On Cross-Diffusion Systems for Two Populations Subject to a Common Congestion Effect

被引：3
|
作者：
Laborde, Maxime [1 ]
机构：
[1] McGill Univ, Dept Math & Stat, Montreal, PQ, Canada
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2020年 / 81卷 / 03期
关键词：
Wasserstein gradient flows; Jordan-Kinderlehrer-Otto scheme; Crowd motion; Nonlinear cross-diffusion systems; EQUATIONS; UNIQUENESS; EVOLUTION; MODEL; CONVEXITY; EXISTENCE; PRINCIPLE; DYNAMICS;
D O I：
10.1007/s00245-018-9527-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the existence of solution for systems of Fokker-Planck equations coupled through a common nonlinear congestion. Two different kinds of congestion are considered: a porous media congestion or soft congestion and the hard congestion given by the constraint rho 1+rho 2 <= 1. We show that these systems can be seen as gradient flows in a Wasserstein product space and then we obtain a constructive method to prove the existence of solutions. Therefore it is natural to apply it for numerical purposes and some numerical simulations are included.
引用
收藏
页码：989 / 1020
页数：32
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