Agenda de la FDP

Séminaire d'Analyse

Le jeudi à 10h30 - Salle 1180 (Bât E2)(Tours)
Responsable :
Impact of slow moving vehicles on vehicular traffic: study of a strongly coupled PDE-ODE.
Thibault Liardwww
jeudi 14 février 2019 - 10h45 - Salle 1180 (Bât E2)(Tours)

Résumé :
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.