On entropic solutions to conservation laws coupled with moving bottlenecks

Thibault Liard (1) , Benedetto Piccoli (2)

1 DEUSTO - Universidad de Deusto
2 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"

Moving bottlenecks in road traffic represent an interesting mathematical problem, which can be modeled via coupled PDE-ODE systems. We consider the case of a scalar conservation law modeling the evolution of vehicular traffic and an ODE with discontinuous right-hand side for the bottleneck. The bottleneck usually corresponds to a slow moving vehicle influencing the bulk traffic flow via a moving flux pointwise constraint. The definition of solutions requires a special entropy condition selecting nonclassical shocks and we prove existence of such solutions for initial data with bounded variation. Approximate solutions are constructed via the wave-front tracking method and their limit are solutions of the Cauchy problem PDE-ODE.

Mots clés: Scalar conservation laws with constraints; Wave-front tracking; Traffic flow modeling; non-classical shocks

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Thibault Liard, Benedetto Piccoli. On entropic solutions to conservation laws coupled with moving bottlenecks. 2019. ⟨hal-02149946⟩