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Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid

Author

Listed:
  • Tingting Chen

    (School of Mathematics and Computer Sciences, Jianghan University, Wuhan 430056, China)

  • Weifeng Jiang

    (Key Laboratory of Intelligent Manufacturing Quality Big Data Tracing and Analysis of Zhejiang Province, College of Science, China Jiliang University, Hangzhou 310018, China)

  • Tong Li

    (Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA)

  • Zhen Wang

    (Center for Mathematical Sciences, Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China)

  • Junhao Lin

    (Key Laboratory of Intelligent Manufacturing Quality Big Data Tracing and Analysis of Zhejiang Province, College of Science, China Jiliang University, Hangzhou 310018, China)

Abstract

We are concerned with the Riemann problem for the isentropic Euler equations of mixed type in the dark energy fluid. This system is non-strictly hyperbolic on the boundary curve of elliptic and hyperbolic regions. We obtain the unique admissible shock waves by utilizing the viscosity criterion. Assuming fixed left states are in the elliptic and hyperbolic regions, respectively, we construct the unique Riemann solution for the mixed-type models with the initial right state in some feasible regions. Finally, we present numerical simulations which are consistent with our theoretical results.

Suggested Citation

  • Tingting Chen & Weifeng Jiang & Tong Li & Zhen Wang & Junhao Lin, 2024. "Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid," Mathematics, MDPI, vol. 12(16), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2444-:d:1451181
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    References listed on IDEAS

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    1. Shah, Sarswati & Singh, Randheer & Jena, Jasobanta, 2022. "Steepened wave in two-phase Chaplygin flows comprising a source term," Applied Mathematics and Computation, Elsevier, vol. 413(C).
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