Existence of BV solutions for a non-conservative constrained Aw-Rascle-Zhang model for vehicular traffic

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:467

Article

Dymski, Nikodem S.^1,2  Goatin, Paola²  Rosini, Massimiliano D.^1,3 

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

[2] Univ Cote dAzur, Inria Sophia Antipolis Mediterranee, INRIA, CNRS,LJAD, 2004,Route Lucioles BP 93, F-06902 Sophia Antipolis, France

[3] Univ Ferrara, Dipartimento Matemat & Inform, Via Machiavelli 35, I-44121 Ferrara, Italy

关键词: Hyperbolic systems of conservation laws;    Local flux constraint;    Wave-front tracking;    Traffic flow modeling;   

DOI  :  10.1016/j.jmaa.2018.07.025

来源: Elsevier

【 摘 要 】

The main aim of this paper is to study the Aw-Rascle-Zhang (ARZ) model with non-conservative local point constraint on the density flux introduced in [10], its motivation being, for instance, the modeling of traffic across a toll gate. We prove the existence of weak solutions under assumptions that result to be more general than those required in [11]. More precisely, we do not require that the waves of the first characteristic family have strictly negative speeds of propagation. The result is achieved by showing the convergence of a sequence of approximate solutions constructed via the wave-front tracking algorithm. The case of solutions attaining values at the vacuum is considered. We also present an explicit numerical example to describe some qualitative features of the solutions. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free