Riemann solutions to the logotropic system with a Coulomb-type friction

Abstract

The motivation of this study is to analyze the structure of the Riemann solutions for compressible hyperbolic system, so called logotropic system, with a Coulomb-type friction. The classical wave solutions of the Riemann problem (RP) for the logotropic system are structured explicitly for all cases. The system considered in this problem is hyperbolic in nature and the characteristic fields associated with the characteristics are genuinely nonlinear. It is shown that the Riemann solutions for the logotropic system with a Coulomb-type friction term composed of the rarefaction wave and shock wave. It is found that the Coulomb-type friction term, appearing in the governing equations, influences the Riemann solution for the logotropic system.

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Acknowledgements

The authors are very grateful to the referees for their valuable suggestions which have signicantly improved the manuscript.

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Correspondence to Rahul Kumar Chaturvedi.

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Chaturvedi, R.K., Singh, L.P. Riemann solutions to the logotropic system with a Coulomb-type friction. Ricerche mat (2020). https://doi.org/10.1007/s11587-020-00526-4

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Keywords

  • Riemann problem
  • Hyperbolic system
  • Shock wave
  • Friction

Mathematics Subject Classification

  • 35L03
  • 35L40
  • 76L05
  • 70F40