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arXiv · 1410.1110

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

Jinhuan Wang·Jinjing Liu·Hanchun Yang
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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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Jinhuan Wang, Jinjing Liu, Hanchun Yang. 2014-10-05. Vanishing Pressure Limit of Solutions to the Aw-Rascle Model for Modified Chaplygin gas. https://arxiv.org/abs/1410.1110

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