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Wave Interactions and Stability of Riemann Solutions to the Aw-Rascle Model with Friction for Modified Chaplygin Gas

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Abstract

We study wave interactions and stability of Riemann solutions to the inhomogeneous Aw-Rascle (AR) model with Coulomb-like friction term for modified Chaplygin gas. First, the Riemann problem with initial data of two piecewise constants is technically solved by introducing some variable transformation. It is found that the Riemann solutions for the inhomogeneous system are no longer self-similar, and all the elementary waves are bent into parabolic shapes. Second, by investigating the interactions of elementary waves, the global structures of Riemann solutions to the inhomogeneous AR model with perturbed three-piecewise-constant initial data are established constructively. Moreover, we show that the solutions are stable under the small perturbation of initial data.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan Normal University, Kunming, 650500, People’s Republic of China

    Shuai Fan & Yu Zhang

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  1. Shuai Fan
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  2. Yu Zhang
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Correspondence to Yu Zhang.

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Supported by Yunnan Fundamental Research Projects (202101AT070128, 2018FD015) and Scientific Research Foundation Project of Yunnan Education Department (2018JS150).

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Fan, S., Zhang, Y. Wave Interactions and Stability of Riemann Solutions to the Aw-Rascle Model with Friction for Modified Chaplygin Gas. Bull Braz Math Soc, New Series 53, 765–785 (2022). https://doi.org/10.1007/s00574-021-00282-5

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  • DOI: https://doi.org/10.1007/s00574-021-00282-5

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