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Zero-exponent Limit to the Extended Chaplygin Gas Equations with Friction

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Abstract

The exact solutions to the Riemann problem for an inhomogeneous extended Chaplygin gas equations with friction are constructed explicitly. Compared to the homogeneous system, the Riemann solutions for the inhomogeneous one are no longer self-similar. Then, as the two exponents vanish wholly or partly, two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock waves are identified and investigated. It is rigorously proved that as the pressure tends to a constant, the Riemann solutions of the inhomogeneous extended Chaplygin gas equations converge to those of the zero-pressure flow with a body force, while as the pressure approaches some special generalized Chaplygin gas, the Riemann solutions of the inhomogeneous extended Chaplygin gas equations tend to those of the generalized Chaplygin gas equations with the same source term.

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Acknowledgements

This work was supported by NSF of China (11501488), Scientific Research Foundation Project of Yunnan Education Department (2018JS150), Yunnan Applied Basic Research Projects (2018FD015), Nan Hu Young Scholar Supporting Program of XYNU, Science and Technology Foundation of Hebei Education Department (QN2018307) and Natural Science Foundation of Hebei Province (A2019105110).

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Authors and Affiliations

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

    Yu Zhang

  2. College of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, People’s Republic of China

    Yanyan Zhang

  3. Department of Mathematics and Information Science, Tangshan Normal University, Tangshan, 063000, People’s Republic of China

    Jinhuan Wang

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  1. Yu Zhang
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  2. Yanyan Zhang
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  3. Jinhuan Wang
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Correspondence to Yu Zhang.

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Zhang, Y., Zhang, Y. & Wang, J. Zero-exponent Limit to the Extended Chaplygin Gas Equations with Friction. Bull. Malays. Math. Sci. Soc. 44, 3571–3599 (2021). https://doi.org/10.1007/s40840-021-01133-8

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  • DOI: https://doi.org/10.1007/s40840-021-01133-8

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