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Volume 12
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Article

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

by
Tingting Chen
1,
Weifeng Jiang
2,*,
Tong Li
3,
Zhen Wang
4 and
Junhao Lin
2
1
School of Mathematics and Computer Sciences, Jianghan University, Wuhan 430056, China
2
Key Laboratory of Intelligent Manufacturing Quality Big Data Tracing and Analysis of Zhejiang Province, College of Science, China Jiliang University, Hangzhou 310018, China
3
Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA
4
Center for Mathematical Sciences, Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(16), 2444; https://doi.org/10.3390/math12162444
Submission received: 9 July 2024 / Revised: 3 August 2024 / Accepted: 5 August 2024 / Published: 6 August 2024
(This article belongs to the Section C1: Difference and Differential Equations)
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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.
Keywords: conservation laws; Riemann problem; mixed type; shock waves conservation laws; Riemann problem; mixed type; shock waves

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MDPI and ACS Style

Chen, T.; Jiang, W.; Li, T.; Wang, Z.; Lin, J. Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid. Mathematics 2024, 12, 2444. https://doi.org/10.3390/math12162444

AMA Style

Chen T, Jiang W, Li T, Wang Z, Lin J. Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid. Mathematics. 2024; 12(16):2444. https://doi.org/10.3390/math12162444

Chicago/Turabian Style

Chen, Tingting, Weifeng Jiang, Tong Li, Zhen Wang, and Junhao Lin. 2024. "Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid" Mathematics 12, no. 16: 2444. https://doi.org/10.3390/math12162444

APA Style

Chen, T., Jiang, W., Li, T., Wang, Z., & Lin, J. (2024). Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid. Mathematics, 12(16), 2444. https://doi.org/10.3390/math12162444

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