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Delta-shocks and vacuums in Riemann solutions to the Umami Chaplygin Aw–Rascle model

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  • Li, Shiwei
  • Wang, Hui

Abstract

This paper is concerned with the formation of delta-shocks and vacuum states for zero-pressure Euler equations. With the introduction of the Umami Chaplygin gas, the Riemann problem for Aw–Rascle model with the reasonable flux-function is solved analytically. The three kinds of Riemann solutions involving the delta-shock are obtained. The generalized Rankine–Hugoniot relation and entropy condition for delta-shock are clarified. Under the entropy condition, the existence and uniqueness of the delta-shock solution are established by solving the generalized Rankine–Hugoniot relation. It is rigorously shown that as the Umami Chaplygin gas pressure and flux-function approach to zero simultaneously, the Riemann solutions of the considered model converge to these of the zero-pressure Euler equations. The numerical results support the theoretical analysis in the end.

Suggested Citation

  • Li, Shiwei & Wang, Hui, 2024. "Delta-shocks and vacuums in Riemann solutions to the Umami Chaplygin Aw–Rascle model," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010658
    DOI: 10.1016/j.chaos.2024.115513
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    References listed on IDEAS

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    1. Gan Yin & Jianjun Chen, 2018. "Existence and Stability of Riemann Solution to the Aw-Rascle Model with Friction," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(4), pages 671-688, December.
    2. Chavanis, Pierre-Henri & Sire, Clément, 2007. "Logotropic distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 140-158.
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