[1] Crighton D G. Model equation of nonlinear acoustics. A Rev Fluid Mech, 1979, 11: 11-33
[2] Crighton D G, Scott J F. Asymptotic solutions of model equations in nonlinear acoustics. Phil Trans R
Soc Lond, 1979, 292A: 101-134
[3] Ding Xiaxi, Wang Jinghua. Global solutions for a semilinear parabolic system. Acta Mathematica Scientia,
1983, 3(3): 397-414
[4] Goodman J. Nonlinear asymptotic stability of viscous shock profile for conservation laws. Arch Rat Mech
Anal, 1986, 95: 325-344
[5] Harabetian E. Rarefaction and large time behavior for parabolic equation and monotone schmes. Comm
Math Phys, 1998, 14: 527-536
[6] Hattori Y, Nishihara K. A note on the stability of the rarefaction wave of the Burgers equation. Japan J
Indust Appl Math, 1991, 8: 85-96
[7] Hopf E. The partial differenatial equation ut + uux = µuxx. Comn Pure Appl Math, 1950, 3: 201-230
[8] Ito K. Asymptotic decay toward the planar rarefaction waves of solution for viscous conservation laws in
several space dimension. Math Models Methods Appl Sci, 1996, 6: 315-338
[9] Il’in A M, Oleinik O A. Asymptotic behavior of the solution of the Cauchy problem for certain quasilinear
equations for large time. Math USSR Sb, 1960, 51: 191-216
[10] Kawashima S, Matsumura A. Asymptotic stability of traveling wave soluyions of systems for one-simentinal
gas motion. Commun Math Phys, 1985, 101: 97-127
[11] Liu T P. Nonlinear stability of shock waves for viscous conservation laws. Mem AMS, 1985, 328: 1-108
[12] Liu T P, Matsumura A, Nishihara K. Behavior of solutions for the Burgers equation with boundary
corresponding to rarefaction waves. SIAM J Math Anal, 1998, 29: 293-308
[13] Matsumura A, Nishihara K. Asymptotic toward the rarefaction waves of the solution of Burgers equation
with nonlinear degenerate viscosity. Nonlinear Analysis, Theory, Methods & Applications, 1994, 23: 605-
614
[14] Matsumura A, Nishihara K. Global stability of rarefaction waves of a one-dimention model system for
compressible viscious gas. Comm Math Phys, 1992, 144: 325-335
No.1 Xu & Jiang: ASYMPTOTIC STABILITY OF RAREFACTION WAVE 129
[15] Matsumura A, Nishhara K. Asymptotic toward the rarefaction waves of the solution of a gas one-dimension
model system for compressible viscious gas. Jaoan J Appl Math, 1986, 3: 1-13
[16] Nishihara K. Asymptotic behaviors of solutions to viscous conservation laws via the L2-energy method.
Lectures note deliverd in Summer School in Fudan University, Shanghai, China, 1999
[17] Nishihara K. A note on the stability of travelling wave solution of Burgers equation. Japan Appl Math,
1985, 2: 27-35
[18] Nishikawa M, Nishihara K. Asymptotic toward the planar rarefaction wave for viscous conservation law in
space dimentions. Trans AMS, 2000, 352: 1203-1215
[19] Smoller J. Shock Waves and Reaction-Diffusion Equation. New York, Berlin: Springer-Verlag, 1983
[20] Scott J F. The long time asymptotic of solution to the generalized Burgers eqution. Proc Roy Soc Lond,
1981, 373A: 443-456
[21] Sauchder P L. Nonlinear Diffusive Waves. New York: Cambridge University Press, 1987
[22] Wang Jinhua, Zhang Hui. A new viscous regulation of the Riemann problem for Burgers equation. J
Differential Equations, 2000, 13(3): 253-263
[23] Wang Z A. Large Behavior of Solution for the Generalized Korteweg-de Vries-Burgers Equation.
[Master’s
thesis]. Central China Normal Univerity, April 2001
[24] Whithman G. Linear and Nonlinear Waves. Wiley-Interscience, 1974
[25] Zhu C J. Quaslinear Hyperbolic Systems with Dissipation Effects.
[Ph.D thesis]. City University of Hong
Kong, Feburary 1999
[26] Zhu C J. Asymptotic behavior of solutions for p-system with relaxation. J Differential Equations, 2002,
180 : 273-306
[27] Zhao Huijiang, Zhu Changjiang, Yu Zhong. Existence and convergence of solutions to a singular perturbed
higher order partial differential equation. Nonlinear Analysis, TMA, 1995, 24: 1435-1455
[28] Zhang Hui. Existence of weak solutions for a degenerate generalized Burgers equation with large initial
data. Acta Mathematica Scientia, 2002, 22B(2): 241-248
|