Non-local multi-class traffic flow models

We prove the existence for small times of weak solutions for a class of non-local systems in one space dimension, arising in traffic modeling. We approximate the problem by a Godunov type numerical scheme and we provide uniform L ∞ and BV estimates for the sequence of approximate solutions. We final...

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Bibliographic Details
Published in:Networks and heterogeneous media 2019, Vol.14 (2), p.371-387
Main Authors: Angela Chiarello, Felisia, Goatin, Paola
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematics
Numerical Analysis
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Summary:We prove the existence for small times of weak solutions for a class of non-local systems in one space dimension, arising in traffic modeling. We approximate the problem by a Godunov type numerical scheme and we provide uniform L ∞ and BV estimates for the sequence of approximate solutions. We finally present some numerical simulations illustrating the behavior of different classes of vehicles and we analyze two cost functionals measuring the dependence of congestion on traffic composition.
ISSN:1556-181X
1556-1801
1556-181X
DOI:10.3934/nhm.2019015