Conservation laws with moving constraints arising in traffic modeling

Abstract: We consider the Cauchy problem for strongly coupled PDE-ODE systems modelling the influence of controlled single vehicles or platoons on the surrounding road traffic. The models consist of a conservation law with discontinuous flux describing the main traffic evolution and ODEs accounting for the trajectories of the slower vehicles, which depend on the downstream traffic conditions. The moving constraint is operated by an inequality on the flux, which accounts for the bottleneck created on the road by the presence of the controlled vehicles. We present some analytical results and a finite volume scheme able to capture exactly the non-classical discontinuities that may arise at the constraint position. Optimal control problems for traffic management are also addressed numerically.

Le mardi 14 octobre 2025 à 11h00 / Amphithéâtre François Canac, LMA

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