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

Autor: Shouqiong Sheng, Zhiqiang Shao
Rok vydání: 2022
Předmět:
Zdroj: Asymptotic Analysis. 129:179-213
ISSN: 1875-8576
0921-7134
DOI: 10.3233/asy-211725
Popis: 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.
Databáze: OpenAIRE
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