Instabilities in generic second-order traffic models with relaxation

被引：0
|
作者：
Goatin, Paola [1 ]
Rizzo, Alessandra [2 ]
机构：
[1] Univ Cote Azur, Inria, CNRS, LJAD, 2004 Route Lucioles,BP 93, F-06902 Sophia Antipolis, France
[2] Univ Studi Messina, Dept Math & Comp Sci Phys Sci & Earth Sci, Viale F Stagno DAlcontres 31, I-98166 Messina, Italy
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2024年 / 75卷 / 05期
关键词：
Macroscopic traffic flow models; Hyperbolic systems of conservation laws; Relaxation; Sub-characteristic condition; ZERO RELAXATION; KINEMATIC WAVES; FLOW; DISSIPATION; VEHICLES; LIMIT;
D O I：
10.1007/s00033-024-02307-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove the existence of weak solutions for a class of second-order traffic models with relaxation, without requiring the sub-characteristic stability condition to hold. With the help of numerical simulations, we show how, in this unstable setting, large but bounded oscillations may arise from small perturbations of equilibria, thus reproducing the formation of stop-and-go waves commonly observed in traffic dynamics. An analysis of the corresponding traveling waves completes the study.
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页数：23
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