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arXiv · 1904.03462

Concentration in vanishing adiabatic exponent limit of solutions to the Aw-Rascle traffic model

Shouqiong Sheng·Zhiqiang Shao
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Abstract

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 $\gamma$ 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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Shouqiong Sheng, Zhiqiang Shao. 2019-04-06. Concentration in vanishing adiabatic exponent limit of solutions to the Aw-Rascle traffic model. https://arxiv.org/abs/1904.03462

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