513
|
RWTH Publication No: 819912 2021   IGPM513.pdf |
TITLE |
Entropy Dissipation at the Junction for Macroscopic Traffic Flow Models |
AUTHORS |
Yannick Holle |
ABSTRACT |
A maximum entropy dissipation problem at a traffic junction and the corresponding
coupling condition are studied. We prove that this problem is equivalent to a coupling condition
introduced by Holden and Risebro. An L1-contraction property of the coupling condition and
uniqueness of solutions to the Cauchy problem are proven. Existence is obtained by a kinetic approximation of Bhatnagar-Gross-Krook-type together with a kinetic coupling condition obtained by a kinetic maximum entropy dissipation problem. The arguments do not require TV-bounds
on the initial data compared to previous results. We also discuss the role of the entropies involved in the macroscopic coupling condition at the traffic junction by studying an example. |
KEYWORDS |
vehicular traffic flow, maximum entropy dissipation, LWR traffix model, scalar conservationlaws, kinetic model, traffic networks |
DOI |
10.1137/21M1423920 |
PUBLICATION |
SIAM Journal on Mathematical AnalysisVol. 54, Iss. 1 (2022) |