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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University of Science & Technology, Hangzhou, 310023, China

    Gan Yin & Jianjun Chen

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  1. Gan Yin
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  2. Jianjun Chen
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Correspondence to Gan Yin.

Additional information

This work is partially supported by National Natural Science Foundation of China (11461066, 11761068) and the Natural Science Foundation of Xinjiang (Grant Nos. 2017D01C053).

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Yin, G., Chen, J. Existence and Stability of Riemann Solution to the Aw-Rascle Model with Friction. Indian J Pure Appl Math 49, 671–688 (2018). https://doi.org/10.1007/s13226-018-0294-3

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  • DOI: https://doi.org/10.1007/s13226-018-0294-3

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