Entropy admissibility of the limit solution for a nonlocal model of traffic flow

Abstract

We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density ahead. The averaging kernel is of exponential type: w(s) = -1 e -s/ . For any decreasing velocity function v, we prove that, as 0, the limit of solutions to the nonlocal equation coincides with the unique entropy-admissible solution to the scalar conservation law t + (v())x = 0.

Topics & Concepts