John M. Hong, Cheng-Hsiung Hsu and Weishi Liu, Inviscid and viscous stationary waves of gas flow through contracting-expanding nozzles , J. Diff. Eqns. 248 (2010), pp. 50-76.
 S. R. Chakravarthy and S. Osher, Numerical experiments with the Osher upwind scheme for the Euler equations, AIAA J. 21 (1983), no. 9, pp. 1241-1248.
 C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, 2nd edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 325, Springer-Verlag, Berlin, 2005. P. Embid, J. Goodman, and A. Majda, Multiple steady states for 1-D transonic flow, SIAM J. Sci. Stat. Comput. 5(1984), no. 1, pp. 21-41.
 N. Fenichel, Persistence and smoothness of invariant manifolds and flows, Indiana Univ. Math. J. 21 (1971/1972), pp. 193-226.
 N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, J. Diff. Eqns. 31 (1979), no. 1, pp. 53-98.
 J. M. Hong, C.-H. Hsu and W. Liu, Viscous standing asymptotic states of isentropic compressible flows through a nozzle, Arch. Ration. Mech. Anal. 196 (2010), no. 2, pp. 575-597.
 J. M. Hong, C.-H. Hsu and W.Liu, Sub-to-super transonic steady states and their linear stabilities for gas flows, submitted.
 M. Hirsch, C. Pugh, and M. Shub, Invariant Manifolds, Lecture Notes in Math. 583, Springer-Verlag, New York, 1976.
 S.-B. Hsu, and T.-P. Liu, Nonlinear singular Sturm-Liouville problems and an application to transonic flow through a nozzle, Comm. Pure Appl. Math. 43 (1990), no. 1, pp. 31-61.
 E. Isaacson and B. Temple, Convergence of the 2 × 2 Godunov method for a general resonant nonlinear balance law, SIAM J. Appl. Math. 55 (1995), no. 3, pp. 625-640.
 C.K.R.T. Jones, Geometric singular perturbation theory, Dynamical Systems (Montecatini Terme, 1994). Lecture Notes in Math. 1609, Springer-Verlag, Berlin, 1995, pp. 44-118.
 H. W. Liepmann and A. Roshlo, Elementary of Gas Dynamics, GALCIT Aero-nautical Series, New York: Wiely, 1957.
 X.-B. Lin and S. Schecter, Stability of self-similar solutions of the Dafermos regularization of a system of conservation laws, SIAM J. Math. Anal. 35 (2004), no. 4, pp. 884-921.
 T.-P. Liu, Quasilinear hyperbolic system, Comm. Math. Phys. 68 (1979), no. 2, pp. 141-172.
 T. P. Liu Transonic gas flow in a duct of varying area, Arch. Ration. Mech. Anal. 80 (1982), no. 1, pp. 1-18.
 W. Liu, Multiple viscous wave fan profiles for Riemann solutions of hyperbolic systems of conservation laws, Discrete Contin. Dyn. Syst. 10 (2004), no. 4, pp. 871-884.
 S. Schecter, Undercompressive shock waves and the Dafermos regularization, Nonlinearity 15 (2002), no. 4, pp. 1361-1377.
 S. Schecter, Eigenvalues of self-similar solutions of the Dafermos regularization of a system of conservation laws via geometric singular perturbation theory, J. Dynam. Differential Equations 18 (2006), no. 1, pp. 53-101.
 S. Schecter and P. Szmolyan, Composite waves in the Dafermos regularization, J. Dynam. Differential Equations 16 (2004), no. 3, pp. 847-867.
 G. R. Shubin, A. B. Stephens and H. Glaz, Steady shock tracking and Nowton’s method applied to one-dimensional duct flow, J. Comput. Phys. 39 (1980), no. 2, pp. 364-374.
 D. Serre, Systems of conservation laws. 1. Hyperbolicity, entropies, shock waves, Translated from the 1996 French original by I. N. Sneddon. Cambridge University Press, Cambridge, 1999.
 D. Serre, Systems of conservation laws. 2. Geometric structures, oscillations, and initial-boundary value problems, Translated form the 1996 French original by I.N. Sneddon. Cambridge University Press, Cambridge, 2000.
 D. H. Smith, Non-uniqueness and multi-shock solutions for transonic flows, IMA J. Appl. Math. 71 (2006), no. 1, pp. 120-132.
 P. Szmolyan and M. Wechselberger, Canards in R3, J. Diff. Eqns. 177 (2001), no. 2, pp. 419-453.
 B. Whitham Linear and nonlinear waves, New York, John Wiley, 1974.