[1] Huang F M, Li J, Matsumura A. Asymptotic stability of combination of viscous contact wave with rarefaction waves for one-dimenional compressible Navier-Stokes system. Archive for Rational Mechanics and Analysis, 2010, 197:89-116
[2] Ducomet B, Zlotnik A. On the large-time behavior of 1D radiative and reactive viscous flows for higher-order kinetics. Nonlinear Analysis, 2005, 63(8):1011-1033
[3] Smoller J. Shock Waves and Reaction-Diffusion Equations. 2nd ed. New York:Springer-Verlag, 1994
[4] Huang F M, Matsumura A, Xin Z P. Stability of contact discontinuities for the 1-D compressible NavierStokes equations. Archive for Rational Mechanics and Analysis, 2006, 179:55-77
[5] Hsiao L, Liu T P. Nonlinear diffusive phenomena of nonlinear hyperbolic systems. Chinese Annals of Mathematics, Series A, 1993, 14:465-480
[6] Duyn C J, Peletier L A. A class of similarity solutions of the nonlinear diffusion equation. Nonlinear Analysis, 1977, 1:223-233
[7] Xin Z P. On nonlinear stability of contact discontinuities//Hyperbolic Problems:Theory, Numerics, Applications. River Edge:World Scientific, 1996:249-257
[8] Liu T P, Xin Z P. Pointwise decay to contact discontinuities for systems of viscous conservation laws. The Asian Journal of Mathematics, 1997, 1:34-84
[9] Xin Z P, Zeng H H. Pointwise stability of contact discontinuity for viscous conservation laws with general perturbations. Communications in Partial Differential Equations, 2010, 35:1326-1354
[10] Huang F M, Matsumura A, Shi X D. On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary. Osaka Journal of Mathematics, 2004, 41:193-210
[11] Chen Z Z, Xiao Q H. Nonlinear stability of viscous contact wave for the one-dimensional compressible fluid models of Korteweg type. Mathematical Methods in the Applied Sciences, 2013, 36:2265-2279
[12] Huang B K, Liao Y K. Global stability of viscous contact wave with rarefaction waves for compressible Navier-Stokes equations with temperature-dependent viscosity. Mathematical Models and Methods in Applied Sciences, 2017, 27:2321-2379
[13] Huang F M, Wang T. Stability of superposition of viscous contact wave and rarefaction waves for compressible Navier-Stokes system. Indiana University Mathematics Journal, 2016, 65(6):1833-1875
[14] Huang F M, Xin Z P, Yang T. Contact discontinuity with general perturbation for gas motions. Advances in Mathematics, 2008, 219:1246-1297
[15] Huang F M, Zhao H J. On the global stability of contact discontinuity for compressible Navier-Stokes equations. Rendiconti del Seminario Matematico della Università di Padova, 2003, 109:283-305
[16] Wan L, Wang T, Zhao H J. Asymptotic stability of wave patterns to compressible viscous and heatconducting gases in the half-space. Journal of Differential Equations, 2016, 261:5949-5991
[17] Huang F M, Wang Y, Zhai X Y. Stability of viscous contact wave for compressible Navier-Stokes system of general gas with free boundary. Acta Mathematica Scientia, 2010, 30B(6):1906-1919
[18] Zeng H H. Stability of a superposition of shock waves with contact discontinuities for systems of viscous conservation laws. Journal of Differential Equations, 2009, 246:2081-2102
[19] Hong H. Global stability of viscous contact wave for 1-D compressible Navier-Stokes equations. Journal of Differential Equations, 2012, 252:3482-3505
[20] Duan R J, Liu H X, Zhao H J. Nonlinear stability of rarefaction waves for the compressible Navier-Stokes equations with large initial perturbation. Transactions of the American Mathematical Society, 2009, 361(1):453-493
[21] Fan L L, Liu H X, Wang T, et al. Inflow problem for the one-dimensional compressible Navier-Stokes equations under large initial perturbation. Journal of Differential Equations, 2014, 257:3521-3553
[22] Liu H X, Yang T, Zhao H J, et al. One-dimensional compressible Navier-Stokes equations with temperature dependent transport coefficients and large data. SIAM Journal on Mathematical Analysis, 2014, 46:2185-2228
[23] Liao Y K, Zhao H J. Global solutions to one-dimensional equations for a self-gravitating viscous radiative and reactive gas with density-dependent viscosity. Communications in Mathematical Science, 2017, 15(5):1423-1456
[24] Ducomet B. A model of thermal dissipation for a one-dimensional viscous reactive and radiative gas. Mathematical Methods in the Applied Sciences, 1999, 22(15):1323-1349
[25] Jiang J, Zheng S. Global well-posedness and exponential stability of solutions for the viscous radiative and reactive gas. Zeitschrift fur Angewandte Mathematik und Physik, 2014, 65(4):645-686
[26] Jiang J, Zheng S. Global solvability and asymptotic behavior of a free boundary problem for the onedimensional viscous radiative and reactive gas. Journal of Mathematical Physics, 2012, 53(12):123704
[27] Qin Y, Hu G, Wang T. Global smooth solutions for the compressible viscous and heat-conductive gas. Quarterly of Applied Mathematics, 2011, 69(3):509-528
[28] Umehara M, Tani A. Global solution to the one-dimensional equations for a self-gravitating viscous radiative and reactive gas. Journal of Differential Equations, 2007, 234(2):439-463
[29] Umehara M, Tani A. Global solvability of the free-boundary problem for one-dimensional motion of a self gravitating viscous radiative and reactive gas. Proceedings of the Japan Academy, Ser. A, Mathematical Sciences, 2008, 84(7):123-128
[30] Ducomet B, Zlotnik A. Lyapunov functional method for 1D radiative and reactive viscous gas dynamics. Archive for Rational Mechanics and Analysis, 2005, 177(2):185-229
[31] Liao Y K, Zhao H J. Global existence and large-time behavior of solutions to the Cauchy problem of onedimensional viscous radiative and reactive gas. Journal of Differential Equations, 2018, 265:2076-2120
[32] Donatelli D, Trivisa K. On the motion of a viscous compressible radiative-reacting gas. Communications in Mathematical Physics, 2006, 265(2):463-491
[33] Zhang J. Remarks on global existence and exponential stability of solutions for the viscous radiative and reactive gas with large initial data. Nonlinearity, 2017, 30(4):1221-1261
[34] Qin Y, Zhang J, Su X, et al. Global existence and exponential stability of spherically symmetric solutions to a compressible combustion radiative and reactive gas. Journal of Mathematical Fluid Mechanics, 2016, 18(3):415-461
[35] Umehara M, Tani A. Temporally global solution to the equations for a spherically symmetric viscous radiative and reactive gas over the rigid core. Analysis and Applications, 2008, 6(2):183-211
[36] Liao Y K, Wang T, Zhao H J. Global spherically symmetric flows for a viscous radiative and reactive gas in an exterior domain. Journal of Differential Equations, 2019, 266:6459-6506
[37] Williams F A. Combustion Theory. Reading, MA:Addison-Wesley, 1965
[38] Chen G Q. Global solutions to the compressible Navier-Stokes equations for a reacting mixture. SIAM Journal on Mathematical Analysis, 1992, 23:609-634
[39] Chen G Q, Hoff D, Trivisa K. On the Navier-Stokes equations for exothermically reacting compressible fluids. Acta Mathematicae Applicatae Sinica English Series, 2002, 18(1):15-36
[40] Chen G Q, Hoff D, Trivisa K. Global solutions to a model for exothermically reacting, compressible flows with large discontinuous initial data. Archive for Rational Mechanics and Analysis, 2003, 166(4):321-358
[41] Li S R. On one-dimensional compressible Navier-Stokes equations for a reacting mixture in unbounded domains. Zeitschrift fur Angewandte Mathematik und Physik, 2017, 68(5):106
[42] Xu Z, Feng Z F. Nonlinear stability of rarefaction waves for one-dimensional compressible Navier-Stokes equations for a reacting mixture. Zeitschrift fur Angewandte Mathematik und Physik, 2019, 70:155
