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

Tingting Chen, Weifeng Jiang (), Tong Li, Zhen Wang and Junhao Lin
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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

Mathematics, 2024, vol. 12, issue 16, 1-20

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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