张莹, 郭俐辉. 广义Chaplygin气体Euler方程组的Riemann问题[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2012, 29(4): 426-430.DOI:
广义Chaplygin气体Euler方程组的Riemann问题
摘要
研究了一维广义Chaplygin气体Euler方程组的Riemann问题.利用特征分析方法
得到了Riemann问题解的存在性和唯一性.和多方气体不同的是
广义Chaplygin气体Euler方程组会出现质量集中的解.
Abstract
This paper is concerned with the Riemann problem of Euler equations for one-dimensional generalized Chaplygin gas.Using characteristic analysis
we get the existence and uniqueness of the Riemann solutions.Different from the polytropic gas
the Euler equations for generalized Chaplygin Gas appear the mass concentration solution.
关键词
Keywords
references
Chaplygin Sergey.On gas jets[J].Sci Mem Moscow Univ Math Phy,1904,21:1-121.
Tsien Hsue-shen.Two dimensional subsonic flow of compressible fluids[J].J Aeron Sci,1939,6:399-407.
Theodore von Karman.Compressibility effects in aerodynamics[J].J Aeron Sci,1941,8:337-365.
Xu Xiaodong,He Jianhua,Wang Bin.Breaking parameter degeneracy in interacting dark energy models from observa-tions[J].Phys Lett B,2011,27:513-519.
Brenier Yann.Solutions with concentration to the Riemann problem for one-dimensional Chaplygin gas equations[J].JMath Fluid Mach,2005,7:S326-S331.
Serre Denis.Multidimensional shock interaction for a Chaplygin gas[J].Anal,2009,191:539-577.
Guo Lihui,Sheng Wancheng,Zhang Tong.The two-dimensional Riemann problem for isentropic Chaplygin gas dynamicsystem[J].Communications on Pure and Applied Analysis,2010,2(9):431-458.
Chang Tung,Hsiao Ling.The Riemann Problem and Interaction of Waves in Gas Dynamics[A].In:John Wiley and Sons.Pitman Monographs and Surveys in Pure and Applied Mathematics No.41[C].United States:New York NY(US),1989.
Sheng Wancheng.Two-Dimensional Riemann Problem for Scalar Conservation Laws[J].J Differential Equations,2002,183:239-261.
Zhang Tong,Zheng Yuxi.Two dimensional Riemann problem for a single conservation laws[J].Trans Amer Math Soc,1989,312:589-619.