scholarly journals Well-posedness of a conservation law with non-local flux arising in traffic flow modeling

2015 ◽  
Vol 132 (2) ◽  
pp. 217-241 ◽  
Author(s):  
Sebastien Blandin ◽  
Paola Goatin
Keyword(s):  
Traffic Flow ◽  
Conservation Law ◽  
Well Posedness ◽  
Flow Modeling ◽  
Non Local

A Hölder continuous ODE related to traffic flow

2003 ◽  
Vol 133 (4) ◽  
pp. 759-772 ◽  
Author(s):  
Rinaldo M. Colombo ◽  
Andrea Marson
Keyword(s):  
Vector Field ◽  
Initial Data ◽  
Differential Equations ◽  
Traffic Flow ◽  
Conservation Law ◽  
Continuous Dependence ◽  
Well Posedness ◽  
Hölder Continuous ◽  
Scalar Conservation Law ◽  
Scalar Conservation

This paper is devoted to the proof of the well posedness of a class of ordinary differential equations (ODEs). The vector field depends on the solution to a scalar conservation law. Forward uniqueness of Filippov solutions is obtained, as well as their Hölder continuous dependence on the initial data of the ODE. Furthermore, we prove the continuous dependence in C0 of the solution to the ODE from the initial data of the conservation law in L1.This problem is motivated by a model of traffic flow.

scholarly journals A non-local traffic flow model for 1-to-1 junctions

2019 ◽  
Vol 31 (6) ◽  
pp. 1029-1049
Author(s):  
F. A. CHIARELLO ◽  
J. FRIEDRICH ◽  
P. GOATIN ◽  
S. GÖTTLICH ◽  
O. KOLB
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Approximate Solutions ◽  
Well Posedness ◽  
Local Conservation ◽  
Flow Modelling ◽  
Vehicle Density ◽  
Proposed Model ◽  
Non Local ◽  
Traffic Flow Modelling

We present a model for a class of non-local conservation laws arising in traffic flow modelling at road junctions. Instead of a single velocity function for the whole road, we consider two different road segments, which may differ for their speed law and number of lanes (hence their maximal vehicle density). We use an upwind type numerical scheme to construct a sequence of approximate solutions, and we provide uniform L∞ and total variation estimates. In particular, the solutions of the proposed model stay positive and below the maximum density of each road segment. Using a Lax–Wendroff type argument and the doubling of variables technique, we prove the well-posedness of the proposed model. Finally, some numerical simulations are provided and compared with the corresponding (discontinuous) local model.

scholarly journals GPU‐accelerated simulation of a non‐local conservation law

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Simone Göttlich ◽  
Jann Müller ◽  
Jennifer Weissen
Keyword(s):  
Conservation Law ◽  
Local Conservation ◽  
Accelerated Simulation ◽  
Non Local ◽  
Local Conservation Law

scholarly journals A macroscopic traffic flow model with finite buffers on networks: well-posedness by means of Hamilton–Jacobi equations

2020 ◽  
Vol 18 (6) ◽  
pp. 1569-1604
Author(s):  
Nicolas Laurent-Brouty ◽  
Alexander Keimer ◽  
Paola Goatin ◽  
Alexandre M. Bayen
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Well Posedness ◽  
Finite Buffers ◽  
Traffic Flow Model ◽  
Macroscopic Traffic Flow ◽  
Jacobi Equations
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