Séminaire d'AnalyseImpact of slow moving vehicles on vehicular traffic: study of a strongly coupled PDE-ODE.
jeudi 14 février 2019 10:45 - Tours - Salle 1180 (Bât E2)
In the seminal experiments of Sugiyama et al and Tadaki et al., human driving behavior alone was shown to be sufficient to trigger stop and go waves. Motivated by this experiment, we study a coupled PDE-ODE modeling a slow moving vehicle immersed in vehicular traffic. The PDE consists of a scalar conservation laws modeling the traffic flow evolution and the ODE models the trajectory of a slow moving vehicle. The slow moving vehicle influences the bulk traffic flow via a point flux constraint, which is given by an inequality on the flux at the slow vehicle position. We prove existence, uniqueness and continuous dependence of solutions with respect to initial data of bounded variation. The proof is based on a wave front tracking method and a new backward in time method established to capture the values of the norm of generalized tangent vectors at every time. These results are the first step to study control problems for traffic flow via the action of connected autonomous vehicles.