| Issue |
Math. Model. Nat. Phenom.
Volume 18, 2023
|
|
|---|---|---|
| Article Number | 7 | |
| Number of page(s) | 25 | |
| Section | Mathematical methods | |
| DOI | https://doi.org/10.1051/mmnp/2023006 | |
| Published online | 10 March 2023 | |
Traveling solutions for a multi-anticipative car-following traffic model
1
Lebanese American University, Department of computer science and mathematics,
Byblos Campus, P.O. Box 36,
Byblos, Lebanon
2
University of Sfax, Higher Institute of Business Adiministration of Sfax,
3018 Sfax, Tunisia
* Corresponding author: nader.elkhatib@lau.edu.lb
Received:
11
November
2022
Accepted:
6
February
2023
In this paper, we consider a steady state multi-anticipative traffic model and we provide necessarily and sufficient conditions for the existence of traveling solutions. In our work, the word “traveling” means that the distance between two consecutive vehicles travels continuously between two different states. As application to our result, we show that taking a strictly concave optimal velocity, we can construct a traveling solution such that the distance between two vehicles decreases. The existence, uniqueness and the study of the asymptotic behavior of such solutions is done at the level of the Hamilton-Jacobi equation.
Mathematics Subject Classification: 74J40 / 90B20 / 35D40
Key words: Traffic model / Hamilton-Jacobi equation / viscosity solutions / strong comparison principle
© The authors. Published by EDP Sciences, 2023
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