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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 9
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Articles

Riemann problem for Chaplygin gas with combustion

Pages 1877-1887 | Received 22 Nov 2013, Accepted 18 Aug 2014, Published online: 09 Sep 2014

References

  • Courant R, Friedrichs KO. Supersonic flow and shock waves. New York (NY): Interscience; 1948.
  • Chaplygin S. On gas jets. Sci. Mem. Moscow Univ. Math. Phys. 1904;21:1–121.
  • Brenier Y. Solutions with concentration to the Riemann problem for one-dimensional Chaplygin gas equations. J. Math. Fluid Mech. 2005;7:326–331.
  • Guo LH, Sheng WC, Zhang T. The two-dimensional Riemann Problem for isentropic Chaplygin gas dynamics system. Commun. Pure Appl. Anal. 2010;9:431–458.
  • von Karman T. Compressibility effects in aerodynamics. J. Aeron. Sci. 1941;8:337–365.
  • Lai G, Sheng WC, Zheng YX. Simple waves and pressure delta waves for a Chaplygin gas in two-dimensions. Discrete Contin. Dyn. Syst. 2011;31:489–523.
  • Serre D. Multidimensional shock interaction for a Chaplygin gas. Arch. Ration. Mech. Anal. 2009;191:539–577.
  • Tsien HS. Two dimensional subsonic flow of compressible fluids. J. Aeron. Sci. 1939;6:399–407.
  • Williams FA. Combustion theory. Menlo Park (CA): Benjamin Commings; 1985.
  • Zhang T, Zheng YX. Riemann problem for gasdynamic combustion. J. Differ. Equ. 1989;77:203-230.
  • Liu YJ, Sheng WC. Generalized Riemann problem for gas dynamic combustion. Appl. Math. Mech., (Engl. Ed.). 2011;32:1079–1090.
  • Ying LA, Teng ZH. Riemann problem for a reacting and convection hyperbolic system. J. Approx. Theory Appl. 1984;1:95–122.
  • Liu TP, Zhang T. A scalar combustion model. Arch. Ration. Mech. Anal. 1991;114:297–312.
  • Tan DC, Zhang T. Riemann problem for the selfsimilar ZND model in gas dynamical combustion. J. Differ. Equ. 1992;95:331–369.
  • Hsu CH, Lin SS. Some qualitative properties of the Riemann problem in gas dynamical combustion. J. Differ. Equ. 1997;140:10–43.
  • Zhu L. Chaplygin gas dynamic system in adiabatic flow [Master thesis]. Shanghai: Shanghai University; 2010.
  • Sheng WC, Zhang T. The Riemann problem for the transportation equations in gas dynamics. Vol. 137, Providence (RI): Memoirs of the American Mathematical Society. 1999.

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