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Congested traffic dynamics, weak flows and very degenerate elliptic equations

By L. Brasco, G. Carlier and F. Santambrogio

Abstract

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

Topics: Traffic congestion, Weak flows, Superposition solutions, DiPerna–Lions theory, Degenerate PDE's, Regularity
Year: 2010
DOI identifier: 10.1016/j.matpur.2010.03.010
OAI identifier: oai:iris.unife.it:11392/2333286
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