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The Vanishing Pressure Limit of Riemann Solutions to the Non-Isentropic Euler Equations for Generalized Chaplygin Gas

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  • Qixia Ding
  • Lihui Guo

Abstract

We analyze the appearance of delta shock wave and vacuum state in the vanishing pressure limit of Riemann solutions to the non-isentropic generalized Chaplygin gas equations. As the pressure vanishes, the Riemann solution including two shock waves and possible one contact discontinuity converges to a delta shock wave solution. Both the density and the internal energy simultaneously present a Dirac delta singularity. And the Riemann solution involving two rarefaction waves and possible one contact discontinuity converges to a solution involving vacuum state of the transport equations.

Suggested Citation

  • Qixia Ding & Lihui Guo, 2019. "The Vanishing Pressure Limit of Riemann Solutions to the Non-Isentropic Euler Equations for Generalized Chaplygin Gas," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-12, July.
    • Handle: RePEc:hin:jnlamp:5253717
    DOI: 10.1155/2019/5253717
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