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

被引：31

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

页码：261 / 287

页数：27

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