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Preprint 2007-001

Existence of solutions for the Aw–Rascle traffic flow model with vacuum

Marte Godvik and Harald Hanche-Olsen

Abstract: We consider the macroscopic model for traffic flow proposed by Aw and Rascle in [doi:10.1137/S0036139997332099]. The model is a 22 system of hyperbolic conservation laws, or, when the model includes a relaxation term, a 22 system of hyperbolic balance laws. The main difficulty is the presence of vacuum, which makes us unable to control the total variation of the conservative variables. We allow vacuum to appear and prove existence of a weak entropy solution to the Cauchy problem.

Paper:
Available as PDF (322 Kbytes).
Author(s):
Marte Godvik,
Harald Hanche-Olsen,
Publishing information:
The paper has appeared in Journal of Hyperbolic Differential Equations 5 #1 (2008), 45–63 (doi:10.1142/S0219891608001428)
Comments:
Revised 2007-06-12. The title has also changed: It used to be The vacuum state for the Aw–Rascle traffic flow model
Submitted by:
; 2007-01-16.