Congested traffic dynamics, weak flows and very degenerate elliptic equations

Lorenzo Brasco (1, 2) , Guillaume Carlier (1) , Filippo Santambrogio (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Dipartimento di Matematica [Pisa]

Starting from a model of traffic congestion, we introduce a minimal-flow-like variational problem whose solution is characterized by a very degenerate elliptic PDE. We precisely investigate the relations between these two problems, which can be done by considering some weak notion of flow for a related ODE. We also prove regularity results for the degenerate elliptic PDE, which enables us in some cases to apply the DiPerna-Lions theory

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Brasco, Guillaume Carlier, Filippo Santambrogio. Congested traffic dynamics, weak flows and very degenerate elliptic equations. Journal de Mathématiques Pures et Appliquées, 2009, in press. ⟨hal-00417462⟩