Vanishing Pressure Limit of Solutions to the Aw-Rascle Model for Modified Chaplygin gas

2014/10/05 by Wang, Jinhuan, Liu, Jinjing, Yang, Hanchun
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1410.1110

Abstract

This paper analyzes the vanishing pressure limit of solutions to the Aw-Rascle model and the perturbed Aw-Rascle model for modified Chaplygin gas. Firstly, the Riemann problem of the Aw-Rascle model is solved constructively. A special delta shock wave in the limit of Riemann solutions is obtained. Secondly, the Riemann problem of the perturbed Aw-Rascle model is solved analytically. It is proved that, as the pressure tends to zero, any Riemann solution containing two shock wave tends to a delta shock solution to the transport equations; any Riemann solution containing two rarefaction wave tends to a two-contact-discontinuity solution to the transport equations and the nonvacuum intermediate state in between tends to a vacuum state.

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