參考文獻 |
References
[1] 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.
[2] 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.
[3] 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.[4] 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.
[5] N. Fenichel, Persistence and smoothness of invariant manifolds and flows, Indiana Univ. Math. J. 21 (1971/1972), pp. 193-226.
[6] N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, J. Diff. Eqns. 31 (1979), no. 1, pp. 53-98.
[7] 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.
[8] J. M. Hong, C.-H. Hsu and W.Liu, Sub-to-super transonic steady states and their linear stabilities for gas flows, submitted.
[9] M. Hirsch, C. Pugh, and M. Shub, Invariant Manifolds, Lecture Notes in Math. 583, Springer-Verlag, New York, 1976.
[10] 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.
[11] 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.
[12] 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.
[13] H. W. Liepmann and A. Roshlo, Elementary of Gas Dynamics, GALCIT Aero-nautical Series, New York: Wiely, 1957.
[14] 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.
[15] T.-P. Liu, Quasilinear hyperbolic system, Comm. Math. Phys. 68 (1979), no. 2, pp. 141-172.
[16] T. P. Liu Transonic gas flow in a duct of varying area, Arch. Ration. Mech. Anal. 80 (1982), no. 1, pp. 1-18.
[17] 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.
[18] S. Schecter, Undercompressive shock waves and the Dafermos regularization, Nonlinearity 15 (2002), no. 4, pp. 1361-1377.
[19] 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.
[20] S. Schecter and P. Szmolyan, Composite waves in the Dafermos regularization, J. Dynam. Differential Equations 16 (2004), no. 3, pp. 847-867.
[21] 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.
[22] 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.
[23] 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.
[24] D. H. Smith, Non-uniqueness and multi-shock solutions for transonic flows, IMA J. Appl. Math. 71 (2006), no. 1, pp. 120-132.
[25] P. Szmolyan and M. Wechselberger, Canards in R3, J. Diff. Eqns. 177 (2001), no. 2, pp. 419-453.
[26] B. Whitham Linear and nonlinear waves, New York, John Wiley, 1974.
|