[1] Hong H, Huang F. 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(1):389-412
[2] Fan L, Matsumura A. Asymptotic stability of a composite wave of two viscous shock waves for a onedimensional system of non-viscous and heat-conductive ideal gas. J Differential Equations, 2015, 258(4):1129-1157
[3] Hou C, Fan L. Asymptotic stability for the inflow problem of the heat-conductive ideal gas without viscosity. Preprint
[4] Huang F, Wang Y, Zhai X, Stability of viscous contact wave for compressible Navier-Stokes system of general gas with free boundary. Acta Mathematica Scientia, 2010, 30B(6):1906-1916
[5] Huang F, Li J, Matsumura A. Stability of the combination of the viscous contact wave and the rarefaction wave to the compressible Navier-Stokes equations. Arch Rat Mech Anal, 2010, 197(1):89-116
[6] Huang F, Li J, Shi X. Asymptotic behavior of solutions to the full compressible Navier-Stokes equations in the half space. Commun Math Sci, 2010, 8:639-654
[7] Huang F, Matsumura A. Stability of a Composite Wave of Two Viscous Shock Waves for the Full Compresible Navier-Stokes Equation. Comm Math Phys, 2009, 289(3):841-861
[8] Huang F, Matsumura A, Shi X. Viscous shock wave and boundary layer solution to an inflow problem for compressible viscous gas. Comm Math Phys, 2003, 239(1/2):261-285
[9] Huang F, Matsumura A, Xin Z. Stability of Contact discontinuties for the 1-D Compressible Navier-Stokes equations. Arch Ration Mech Anal, 2005, 179(1):55-77
[10] Huang F, Shi X, Wang Y. Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary. Kinet Relat Models, 2010, 3(3):409-425
[11] Huang F, Xin Z, Yang T. Contact discontinuity with general perturbations for gas motions. Adv in Math, 2008, 219(4):1246-1297
[12] Huang F, Zhao H. On the global stability of contact discontinuity for compressible Navier-Stokes equations. Rend Sem Mat Univ Padova, 2003, 109:283-305
[13] Kawashima S, Nakamura T, Nishibata S, et al. Stationary waves to viscous heat-conductive gases in half space:existence, stability and convergence rate. Math Models Methods Appl Sci, 2010, 20(12):2201-2235
[14] Kawashima S, Nishibata S, Zhu P. Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space. Commun Math Phys, 2003, 240(3):483-500
[15] Kawashima S, Zhu P. Asymptotic stability of rarefaction wave for the Navier-Stokes equations for a compressible fluid in the half space. Arch Ration Mech Anal, 2009, 194(1):105-132
[16] Kwon B, Suzuki M, Takayama M. Large-time behavior of solutions to an outflow problem for a shallow water model. J Differential Equations, 2013, 255:1883-1904
[17] Liu H, Yang T, Zhao H, et al. One-dimensional compressible Navier-Stokes equtions with temperature dependent transport coefficients and large data. SIAM J Math Anal, 2014, 46(3):2185-2228
[18] Liu T, Shock waves for Compresible Navier-Stokes Equations are stable. Comm Pure Appl Math, 1986, 39(5):565-594
[19] Matsumura A. Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas. Methods Appl Anal, 2001, 8(4):645-666
[20] Matsumura A. Large-time behavior of solutions for a one-dimensional system of non-viscous and heatconductive ideal gas. Private Communication, 2016
[21] Matsumura A, Mei M. Convergence to travelling fronts of solutions of the p-system with viscosity in the presence of a boundary. Arch Ration Mech Anal, 1999, 146(1):1-22
[22] Matsumura A, Nishihara K. Global asymptotics toward the rarefaction waves for solutions of viscous psystem with boundary effect. Quart Appl Math, 2000, 58(1):69-83
[23] Matsumura A, Nishihara K. Large time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas. Comm Math Phys, 2001, 222(3):449-474
[24] Min L, Qin X. Stability of rarefaction wave for compressible Navier-Stokes equations on the half line. Acta Math Appl Sin Engl Ser, 2016, 32(1):175-186
[25] Nakamura T, Nishibata S. Existence and asymptotic stability of stationary waves for symmetric hyperbolicparabolic systems in half-line. Math Models Methods Appl Sci, 2017, 27(11):2071-2110
[26] Nakamura T, Nishibata S, Usami N. Convergence rate of solutions towards the stationary solutions to symmetric hyperbolic-parabolic systems in half space. Kinet Relat Models, 2018, 11(4):757-793
[27] Nishihara K, Yang T, Zhao H. Nonlinear stability of strong rarefaction waves for compressible Navier-Stokes equations. SIAM J Math Anal, 2004, 35(6):1561-1597
[28] Qin X. Large-time behaviour of solution to the outflow problem of full compressible Navier-Stokes equations. Nonlinearity, 2011, 24(5):1369-1394
[29] Qin X, 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
[30] Qin X, Wang Y. Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations. SIAM J Math Anal, 2011, 43(1):341-366
[31] Rauch J, Massey F. Differentiability of solutions to hyperbolic initial-boundary value problems. Trans Amer Math Soc, 1974, 189:303-318
[32] Zheng S. Nonlinear parabolic equations and hyperbolic-parabolic coupled systems. Longman Group, 1995 |