Journal
ASYMPTOTIC ANALYSIS
Volume 129, Issue 2, Pages 179-213Publisher
IOS PRESS
DOI: 10.3233/ASY-211725
Keywords
Aw-Rascle traffic model; Riemann solutions; delta shock wave; vanishing adiabatic exponent limit; zero pressure gas dynamics; weighted Dirac-measure; numerical simulations
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Funding
- Natural Science Foundation of Fujian Province of China [2019J01642]
- Research Foundation of Fuzhou University [FDJG20190027]
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This paper studies the concentration phenomenon and the formation of delta shock wave in the vanishing adiabatic exponent limit of Riemann solutions to the Aw-Rascle traffic model. It is proven that as the adiabatic exponent tends to zero, the limit of solutions tends to a special delta-shock rather than the classical one in zero pressure gas dynamics. By considering a perturbed Aw-Rascle model, it is rigorously proved that as the adiabatic exponent tends to one, any Riemann solution containing two shock waves tends to a delta-shock to the zero pressure gas dynamics. Representative numerical simulations are also presented to confirm the theoretical analysis.
In this paper, we study the phenomenon of concentration and the formation of delta shock wave in vanishing adiabatic exponent limit of Riemann solutions to the Aw-Rascle traffic model. It is proved that as the adiabatic exponent vanishes, the limit of solutions tends to a special delta-shock rather than the classical one to the zero pressure gas dynamics. In order to further study this problem, we consider a perturbed Aw-Rascle model and proceed to investigate the limits of solutions. We rigorously proved that, as the adiabatic exponent tends to one, any Riemann solution containing two shock waves tends to a delta-shock to the zero pressure gas dynamics in the distribution sense. Moreover, some representative numerical simulations are exhibited to confirm the theoretical analysis.
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