We consider a coupled PDE-ODE model representing a slow moving vehicle immersed in vehicular traffic. The PDE consists of a scalar conservation law modeling the evolution of vehicular traffic and the trajectory of a slow moving vehicle is given by an ODE depending on the downstream traffic density. The slow moving vehicle may be regarded as a moving bottleneck influencing the bulk traffic flow via a moving flux pointwise constraint. We prove existence of solutions with respect to initial data of bounded variation. Approximate solutions are constructed via the wave-front tracking method and their limit are solutions of the Cauchy problem PDE-ODE.
Publié le : 2019-06-06
Classification:
Scalar conservation laws with constraints,
Wave-front tracking,
Traffic flow modeling,
non-classical shocks,
[MATH]Mathematics [math],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-02149946,
author = {Liard, Thibault and Piccoli, Benedetto},
title = {Existence of solutions for scalar conservation laws with moving flux constraints},
journal = {HAL},
volume = {2019},
number = {0},
year = {2019},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-02149946}
}
Liard, Thibault; Piccoli, Benedetto. Existence of solutions for scalar conservation laws with moving flux constraints. HAL, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/hal-02149946/