Open AccessNonlocal reaction traffic flow model with on-off ramps
Author(s) -
Felisia Angela Chiarello,
Harold Deivi Contreras,
Luis Miguel Villada
Publication year - 2022
Publication title -
networks and heterogeneous media
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.732
H-Index - 34
eISSN - 1556-181X
pISSN - 1556-1801
DOI - 10.3934/nhm.2022003
Subject(s) - scalar (mathematics) , mathematics , inflow , flow (mathematics) , combinatorics , physics , geometry , mechanics
We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the inflow and output flow over the on-ramp and off-ramps respectively. We approximate the problem using an upwind-type numerical scheme and we provide \begin{document}$ \mathbf{L^{\infty}} $\end{document} and \begin{document}$ \mathbf{BV} $\end{document} estimates for the sequence of approximate solutions. Together with a discrete entropy inequality, we also show the well-posedness of the considered class of scalar balance laws. Some numerical simulations illustrate the behaviour of solutions in sample cases.