Stability estimates for nonlocal balance laws arising in traffic modelling

Abstract

This paper focuses on the proof of the stability of entropy weak solutions of a nonlocal balance law modeling vehicular traffic flow on a road with on- and off-ramps. The stability is obtained with respect to a kernel function in the source term. We get an estimate of the L1-dependence of the solution with respect to the initial datum, the on-ramp rate, the off-ramp rate and the mentioned kernel function. We also show numerical experiments in order to perform an optimization problem in traffic flow with on-ramps.