Aw-Rascle交通模型解的绝热指数消失极限集中度
Concentration in vanishing adiabatic exponent limit of solutions to the Aw-Rascle traffic model
摘要：
本文研究了Aw-Rascle交通模型的Riemann解的绝热指数极限为零时的集中现象和δ激波的形成。证明了当绝热指数为零时，零压气体动力学解的极限不再是经典解的极限，而是趋向于一种特殊的δ激波。为了进一步研究这个问题，我们考虑了扰动Aw-Rascle模型，并进一步研究了解的极限。严格证明了当$γ$趋于1时，任何包含两个激波的Riemann解在分布意义下趋于零压气体动力学的δ激波。此外，一些有代表性的数值模拟，以证实理论分析。
英文摘要：
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 $γ$ 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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