A TRAFFIC FLOW MODEL WITH NON-SMOOTH METRIC INTERACTION: WELL-POSEDNESS AND MICRO-MACRO LIMIT

被引：30
|
作者：
Goatin, Paola [1 ]
Rossi, Francesco [2 ]
机构：
[1] Inria Sophia Antipolis Mediterranee, Valbonne, France
[2] Aix Marseille Univ, CNRS, ENSAM, Univ Toulon,LSIS UMR 7296, F-13397 Marseille, France
来源：
COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2017年 / 15卷 / 01期
基金：
欧洲研究理事会;
关键词：
Transport equations; non-local velocity; Wasserstein distance; macroscopic traffic flow models; micro-macro limits; WASSERSTEIN DISTANCE; SIMULATION; WAVES;
D O I：
10.4310/CMS.2017.v15.n1.a12
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is obtained recasting the problem in the space of probability measures equipped with the oo-Wasserstein distance. We also show convergence of solutions of a finite dimensional system, which provide a particle method to approximate the solutions to the original problem.
引用
收藏
页码：261 / 287
页数：27
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