Conservation Laws with Nonlocality in Density and Velocity and Their Applicability in Traffic Flow Modelling

被引：0

作者：

Friedrich, Jan ^{[1
]}

Goettlich, Simone ^{[2
]}

Keimer, Alexander ^{[3
]}

Pflug, Lukas ^{[4
]}

机构：

[1] Rhein Westfal TH Aachen, Inst Geometry & Appl Math, D-52064 Aachen, Germany

[2] Univ Mannheim, Dept Math, D-68131 Mannheim, Germany

[3] Friedrich Alexander Univ Erlangen Nurnberg, Dept Math, D-91058 Erlangen, Germany

[4] Friedrich Alexander Univ Erlangen Nurnberg, Competence Unit Sci Comp, D-91058 Erlangen, Germany

来源：

HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, VOL II, HYP2022 | 2024年 / 35卷

关键词：

Nonlocal conservation laws; Traffic flow modelling; Godunov-type scheme; Fixed-point problem; Maximum principle; BALANCE LAWS; UNIQUENESS; EXISTENCE; REGULARITY; LIMIT;

D O I：

10.1007/978-3-031-55264-9_30

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we present a nonlocal conservation law with a velocity depending on an integral term over a part of the space. The model class covers already existing models in literature, but it is also able to describe new dynamics mainly arising in the context of traffic flow modelling. We prove the existence and uniqueness of weak solutions of the nonlocal conservation law. Further, we provide a suitable numerical discretization and present numerical examples.

引用

页码：347 / 357

页数：11

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