Journal
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
Volume 18, Issue -, Pages -Publisher
EDP SCIENCES S A
DOI: 10.1051/mmnp/2023006
Keywords
Traffic model; Hamilton-Jacobi equation; viscosity solutions; strong comparison principle
Ask authors/readers for more resources
In this paper, a steady state multi-anticipative traffic model is considered, and necessary and sufficient conditions for the existence of traveling solutions are provided. The word "traveling" in this work refers to the continuous variation of the distance between two consecutive vehicles between two different states. As an application, it is shown that by taking a strictly concave optimal velocity, a traveling solution can be constructed such that the distance between two vehicles decreases. The existence, uniqueness, and asymptotic behavior of such solutions are studied at the level of the Hamilton-Jacobi equation.
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available