Qualitative analysis of some PDE models of traffic flow

Tong Li; Tong Li

doi:10.3934/nhm.2013.8.773

Networks and Heterogeneous Media

2013, Volume 8, Issue 3: 773-781. doi: 10.3934/nhm.2013.8.773

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Qualitative analysis of some PDE models of traffic flow

Tong Li ^{1
,}

1.
Department of Mathematics, University of Iowa, Iowa City, IA 52242

Received: 01 February 2012 Revised: 01 June 2013
Primary: 35B44, 35L65, 35L67, 35Q35, 76L05, 90B20.

We review our previous results on partial differential equation(PDE) models of traffic flow. These models include the first order PDE models, a nonlocal PDE traffic flow model with Arrhenius look-ahead dynamics, and the second order PDE models, a discrete model which captures the essential features of traffic jams and chaotic behavior. We study the well-posedness of such PDE problems, finite time blow-up, front propagation, pattern formation and asymptotic behavior of solutions including the stability of the traveling fronts. Traveling wave solutions are wave front solutions propagating with a constant speed and propagating against traffic.
- Traffic flow,
- Arrhenius look-ahead dynamics,
- nonlocal flux,
- shock waves,
- blowup criteria,
- traveling waves,
- asymptotic behavior,
- chaos
Citation: Tong Li. Qualitative analysis of some PDE models of traffic flow[J]. Networks and Heterogeneous Media, 2013, 8(3): 773-781. doi: 10.3934/nhm.2013.8.773

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Abstract

We review our previous results on partial differential equation(PDE) models of traffic flow. These models include the first order PDE models, a nonlocal PDE traffic flow model with Arrhenius look-ahead dynamics, and the second order PDE models, a discrete model which captures the essential features of traffic jams and chaotic behavior. We study the well-posedness of such PDE problems, finite time blow-up, front propagation, pattern formation and asymptotic behavior of solutions including the stability of the traveling fronts. Traveling wave solutions are wave front solutions propagating with a constant speed and propagating against traffic.

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