SOLUTIONS OF THE AW-RASCLE-ZHANG SYSTEM WITH POINT CONSTRAINTS

被引：11

作者：

Andreianov, Boris P. ^{[1
,3
]}

Donadello, Carlotta ^{[1
]}

Razafison, Ulrich ^{[1
]}

Rolland, Julien Y. ^{[1
]}

Rosini, Massimiliano D. ^{[2
]}

机构：

[1] Univ Franche Comte, LMB Lab Math CNRS UMR6623, 16 Route Gray, F-25030 Besancon, France

[2] Uniwersytet Marii Curie Sklodowskiej, Inst Matemat, Pl Marii Curie Sklodowskiej 1, PL-20031 Lublin, Poland

[3] Univ Tours, CNRS UMR 7350, LMPT, Parc Grandmont, F-37200 Tours, France

来源：

NETWORKS AND HETEROGENEOUS MEDIA | 2016年 / 11卷 / 01期

关键词：

Road traffic modeling; point constraint; Aw-Rascle and Zhang model; entropies; renormalization; admissible solutions; numerical experiments; TRAFFIC MODEL; EXISTENCE;

D O I：

10.3934/nhm.2016.11.29

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We revisit the entropy formulation and the wave-front tracking construction of physically admissible solutions of the Aw-Rascle and Zhang (ARZ) "second-order" model for vehicular traffic. A Kruzhkov-like family of entropies is introduced to select the admissible shocks. This tool allows to define rigorously the appropriate notion of admissible weak solution and to approximate the solutions of the ARZ model with point constraint. Stability of solutions w.r.t. strong convergence is justified. We propose a finite volumes numerical scheme for the constrained ARZ, and we show that it can correctly locate contact discontinuities and take the constraint into account.

引用

页码：29 / 47

页数：19

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