Journal article
SHOCK FORMATION IN A TRAFFIC FLOW MODEL WITH ARRHENIUS LOOK-AHEAD DYNAMICS
Networks and heterogeneous media, Vol.6(4), pp.681-694
12/01/2011
DOI: 10.3934/nhm.2011.6.681
Abstract
We consider a nonlocal traffic flow model with Arrhenius look-ahead dynamics. We provide a complete local theory and give the blowup alternative of solutions to the conservation law with a nonlocal flux. We show that the finite time blowup of solutions must occur at the level of the first order derivative of the solution. Furthermore, we prove that finite time singularities do occur for several types of physical initial data by analyzing the solutions on different characteristic lines. These results are new and are consistent with the blowups observed in previous numerical simulations on the nonlocal traffic flow model [6].
Details
- Title: Subtitle
- SHOCK FORMATION IN A TRAFFIC FLOW MODEL WITH ARRHENIUS LOOK-AHEAD DYNAMICS
- Creators
- Dong Li - Univ Iowa, Dept Math, Iowa City, IA 52242 USATong Li - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Networks and heterogeneous media, Vol.6(4), pp.681-694
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- DOI
- 10.3934/nhm.2011.6.681
- ISSN
- 1556-1801
- eISSN
- 1556-181X
- Number of pages
- 14
- Grant note
- 0908032 / NSF
- Language
- English
- Date published
- 12/01/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984241047202771
Metrics
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