[1] Duan R, Liu H X, Zhao H J. Nonlinear stability of rarefaction waves for the compressible Navier-Stokes equations with large initial perturbation. Trans Amer Math Soc, 2009, 361:453-493
[2] Goodman J. Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch Ration Mech Anal, 1986, 95:325-344
[3] Hong H H. Global stability of viscous contact wave for 1-D compressible Navier-Stokes equations. J Differential Equations, 2012, 252:3482-3505
[4] Huang F M, Hong H. Asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave for compressible Navier-Stokes equations with free boundary. Acta Mathematica Scientia, 2012, 32B:389-412
[5] Hsiao L, Liu T. Nonlinear diffusive phenomena of nonlinear hyperbolic systems. Chinese Ann Math, 1993, 14B:465-480
[6] Huang F M, Li J, Matsumura A. Asymptotic stability of combination of viscous contact wave with rarefaction waves for one-dimensional compressible Navier-Stokes system. Arch Ration Mech Anal, 2010, 197:89-116
[7] Huang F M, Matsumura A. Stability of a composite wave of two viscous shock waves for the full compressible Navier-Stokes equation. Comm Math Phys, 2009, 289:841-861
[8] Huang F H, Matsumura A, Shi X D. A gas-solid free boundary problem for a compressible viscous gas. SIAM J Math Anal, 2003, 34:1331-1355
[9] Huang F H, Matsumura A, Shi X D. On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary. Osaka J Math, 2004, 41:193-210
[10] Huang F M, Matsumura A, Xin Z P. Stability of contact discontinuities for the 1-D compressible NavierStokes equations. Arch Ration Mech Anal, 2006, 179:55-77
[11] Huang F M, Shi X D, Wang Y. Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary. Kinet Relat Models, 2010, 3(3):409-425
[12] Huang F M, Wang T. Stability of Superposition of Viscous Contact Wave and Rarefaction Waves for Compressible Navier-Stokes System (To appear in Indiana Univ Math J)
[13] Huang F M, Xin Z P, Yang T. Contact discontinuities with general perturbation for gas motion. Adv Math, 2008, 219:1246-1297
[14] Huang F M, Zhao H J. On the global stability of contact discontinuity for compressible Navier-Stokes equations. Rend Sem Mat Univ Padova, 2003, 109:283-305
[15] Jiang S. Large-time behavior of solutions to the equations of a one-dimensional viscous polytropic ideal gas in unbounded domains. Comm Math Phys, 1999, 200:181-193
[16] Jiang S. Remarks on the asymptotic behaviour of solutions to the compressible Navier-Stokes equations in the half-line. Proc Roy Soc Edinburgh Sect A, 2002, 132:627-638
[17] Kawashima S, Matsumura A. Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion. Comm Math Phys, 1985, 101:97-127
[18] Kawashima S, Matsumura A, Nishihara K. Asymptotic behavior of solutions for the equations of a viscous heat-conductive gas. Proc Japan Acad, Ser A, 1986, 62:249-252
[19] Kazhikhov A V. Cauchy problem for viscous gas equations. Siberian Math J, 1982, 23:44-49
[20] Kazhikhov A V, Shelukin V V. Unique global solution with respect to time of initial boundary value problems for one-dimensional equations of a viscous gas. J Appl Math Mech, 1977, 41:273-282
[21] Li J, Liang Z L. Some Uniform Estimates and Large-Time Behavior for One-Dimensional Compressible Navier-Stokes System in Unbounded Domains with Large Data. http://arxiv.org/abs/1404.2214
[22] Liu T P. Shock waves for compressible Navier-Stokes equations are stable. Comm Pure Appl Math, 1986, 39:565-594
[23] Liu T P, Xin Z P. Nonlinear stability of rarefaction waves for compressible Navier-Stokes equations. Comm Math Phys, 1988, 118:451-465
[24] Liu T P, Xin Z P. Pointwise decay to contact discontinuities for systems of viscous conservation laws. Asian J Math, 1997, 1:34-84
[25] Matsumura A. Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas. Hong Kong:Proceedings of IMS Conference on Differential Equations from Mechanics, 1999
[26] Matsumura A, Nishihara K. On the stability of traveling wave solutions of a one-dimensional model system for compressible viscous gas. Japan J Appl Math, 1985, 2:17-25
[27] Matsumura A, Nishihara K. Asymptotics toward the rarefaction wave of the solutions of a one-dimensional model system for compressible viscous gas. Japan J Appl Math, 1986, 3:1-13
[28] Matsumura A, Nishihara K. Global stability of the rarefaction wave of a onedimensional model system for compressible viscous gas. Comm Math Phys, 1992, 144:325-335
[29] Nishihara K, Yang T, Zhao H J. Nonlinear stability of strong rarefaction waves for compressible NavierStokes equations. SIAM J Math Anal, 2004, 35:1561-1597
[30] Qin X H, Wang Y. Stability of wave patterns to the inflow problem of full compressible Navier-Stokes equations. SIAM J Math Anal, 2009, 41(5):2057-2087
[31] Qin X H, Wang Y. Large-time behavior of solutions to the inflow problem of full compress-ible NavierStokes equations. SIAM J Math Anal, 2011, 43:341-366
[32] Smoller J. Shock Waves and Reaction-Diffusion Equations. New York:Springer, 1994
[33] Pan T, Liu H, Nishihara K. Asymptotic behavior of a one-dimensional compressible viscous gas with free boundary. SIAM J Math Anal, 2002, 34:172-291
[34] Szepessy A, Xin Z. Nonlinear stability of viscous shock waves. Arch Rat Mech Anal, 1993, 122(1):53-103
[35] Wan L, Wang T, Zou Q. Stability of stationary solutions to the outflow prob-lem for full compressible Navier-Stokes equations with large initial perturbation. Nonlinearity, 2016, 29(4):1329-1354
[36] Wang T, Zhao H J. Global Large Solutions to a Viscous Heat-Conducting One-Dimensional Gas with Temperature-Dependent Viscosity. Preprint at arXiv:1505.05252, 2015
[37] Xin Z P. On nonlinear stability of contact discontinuities. Hyperbolic problems:theory, numerics, applications. Stony Brook, NY, 1994. River Edge, NJ:World Sci Publishing, 1996:249-257