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Existence and Stability of Riemann Solution to the Aw-Rascle Model with Friction

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  • Gan Yin

    (Zhejiang University of Science & Technology)

  • Jianjun Chen

    (Zhejiang University of Science & Technology)

Abstract

This manuscript is concerned with the Riemann problem and the stability of the Riemann solution of the Aw-Rascle (AR) model with a source term. There exists a unique Riemann solution to the AR model with friction. The problem with three-piecewiseconstant initial data is studied ulteriorly to reach the results on interactions of waves without the vacuum. Based on these results, the Riemann solution turns out to be stable for such a small perturbed initial data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:49:y:2018:i:4:d:10.1007_s13226-018-0294-3
    DOI: 10.1007/s13226-018-0294-3
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    References listed on IDEAS

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    1. Daganzo, Carlos F., 1995. "Requiem for second-order fluid approximations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 277-286, August.
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    Cited by:

    1. 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).

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