[1] Duyn C T, Van Peletier L A. A class of similarity solutions of the nonlinear diffusion equation. Nonlinear
Anal, TMA, 1977, 1: 223-233
[2] Goodman J. Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch Rational
Mech Anal, 1986, 95: 325-344
[3] Grad H. Asymptotic theory of the Boltzmann equation II. In: Laurmann J, ed. Rarefied gas dynamics, 1.
New York: Academic Press, 1963. 26-59
[4] Hsiao L, Liu T P. Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conser-
vation laws with damping. Comm Math Phys, 1992, 143: 599-605
[5] Hsiao L, Luo T. Nonlinear diffusive phenomena of entropy weak solutions for a system of quasilinear
hyperbolic conservation laws with damping. Q Appl Math, 1998, 56: 173-198
[6] Kawashima S, Matsumura A. Asymptotic stability of traveling wave solutions of system for one-dimensional
gas motion. Comm Math Phys, 1985, 101: 97-127
[7] Liu T P. Shock waves for compressible Navier-Stokes equation are stable. Comm Pure Appl Math, 1986,
39: 565-594
[8] Liu T P. Nonlinear stability of shock waves for viscous conservation laws. Mem Amer Math Soc, 1985,
328: 1-128
[9] Matsumura A, Mei M. Nonlinear stability of viscous shock profile for a non-convex system of viscoelasticity.
Osaka J Math, 1997, 34: 589-603
[10] Nishida T. Nonlinear hyperbolic equations and related topics in fliud dynamics. Publications Math´ematiques
D’orsay 78-02, Department de Math´ematique, Universit´e de Paris-Sud, 1978
[11] Nishihara K. Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conser-
vation laws with damping. J Differential Equations, 1996, 131: 171-188
[12] Nishihara K. Stability of traveling waves with degenerate shock for system of one-dimensional viscoelastic
model. J Differential Equations, 1995, 120: 304-318
[13] Nishihara K, Wang W K, Yang T. Lp-convergence rate to nonlinear diffusion waves for p-system with
damping. J Differential Equations, 2000, 161: 191-218
[14] Szepessy A, Xin Z P. Nonlinear stability of viscous shock waves. Arch Rational Mech Anal, 1993, 122:
53-104
[15] Zhao H J. Asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping II. J
Differential Equations, 2000, 167: 467-494
[16] Zhao H J. Convergence to strong nonlinear diffusion waves for solutions of p-system with damping. J
Differential Equations, 2001, 174: 200-236
[17] Zhu C J. Convergence rates to nonlinear diffusion waves for weak entropy solutions to p-system with
damping. Science in China, Series A, 2003, 46(4): 563-575
|