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)