MICRO-MACRO LIMIT OF A NONLOCAL GENERALIZED AW-RASCLE TYPE MODEL

被引：33

作者：

Chiarello, Felisia A. ^{[1
,2
]}

Friedrich, Jan ^{[3
]}

Goatin, Paola ^{[1
]}

Goettlich, Simone ^{[3
]}

机构：

[1] Univ Cote Azur, Inria Sophia Antipolis Mediterranee, INRIA, CNRS,LJAD, F-06902 Sophia Antipolis, France

[2] Politecn Torino, Dept Math Sci GL Lagrange, I-10129 Turin, Italy

[3] Univ Mannheim, D-68131 Mannheim, Germany

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2020年 / 80卷 / 04期

关键词：

traffic flow; second-order models; nonlocal conservation laws; micro-macro limits; TRAFFIC FLOW MODELS; THE-LEADER MODELS; PARTICLE APPROXIMATION; 2ND-ORDER MODEL; WELL-POSEDNESS; WAVES; DERIVATION;

D O I：

10.1137/20M1313337

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a Follow-the-Leader approximation of a nonlocal generalized Aw- Rascle-Zhang (GARZ) model for traffic flow. We prove the convergence to weak solutions of the corresponding macroscopic equations deriving L-infinity and BV estimates. We also provide numerical simulations illustrating the micro-macro convergence and we numerically investigate the nonlocal to local limit for both the microscopic and macroscopic models.

引用

页码：1841 / 1861

页数：21

共 27 条

[1]

[Anonymous], 2015, APPL MATH SCI

[2] Resurrection of "second order" models of traffic flow [J].

Aw, A ;

Rascle, M .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2000, 60 (03) :916-938

[3] Derivation of continuum traffic flow models from microscopic follow-the-leader models [J].

Aw, A ;

Klar, A ;

Materne, T ;

Rascle, M .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2002, 63 (01) :259-278

[4] Well-posedness of a conservation law with non-local flux arising in traffic flow modeling [J].

Blandin, Sebastien ;

Goatin, Paola .

NUMERISCHE MATHEMATIK, 2016, 132 (02) :217-241

[5] Derivation of a first order traffic flow model of Lighthill-Whitham-Richards type [J].

Burger, Michael ;

Goettlich, Simone ;

Jung, Thomas .

IFAC PAPERSONLINE, 2018, 51 (09) :49-54

[6]

Chiarello F. A., EUROPEAN J APPL MATH

[7] GLOBAL ENTROPY WEAK SOLUTIONS FOR GENERAL NON-LOCAL TRAFFIC FLOW MODELS WITH ANISOTROPIC KERNEL [J].

Chiarello, Felisia Angela ;

Goatin, Paola .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2018, 52 (01) :163-180

[8] Stationary wave profiles for nonlocal particle models of traffic flow on rough roads [J].

Chien, Jereme ;

Shen, Wen .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2019, 26 (06)

[9]

Colombo M., 2019, RECENT RESULTS SINGU, P1

[10] On the micro-macro limit in traffic flow [J].

Colombo, R. M. ;

Rossi, E. .

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2014, 131 :217-235

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