Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (1): 47-54.doi: 10.1016/S0252-9602(10)60021-5
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LIU Yan-Hong
Received:
2008-08-28
Online:
2010-01-20
Published:
2010-01-20
Supported by:
The research was supported by the NSF of China (10625105, 10431060) and the Program for New Centary Excellent Talents in University
(NCEF-04-0745).
CLC Number:
LIU Yan-Hong. DECAY RATES OF PLANAR VISCOUS RAREFACTION WAVE FOR MULTI-DIMENSIONAL SCALAR CONSERVATION LAW #br# WITH DEGENERATE VISCOSITY ON HALF SPACE[J].Acta mathematica scientia,Series B, 2010, 30(1): 47-54.
[1] Chen J, Zhu C J. Decay rates of strong planar rarefaction waves to scalar conservation laws with degenerate viscosity in several space [2] Chen J, Liu Y H. Decay rates of solutions for the Burgers equation with boundary corresponding to rarefaction waves. Nonlinear Studies, 2006, 13(2): 141--153 [3] Grighton D G. Model equation of nonlinear acoustics. A Rev Fluid Mech, 1979, 11: 11--33 [4] Grighton D G, Scott J F. Asymptotic solutions of model equations in nonlinear acoustics. Phil Trans R Soc Lond, 1979, 292A: 101--134 [5] Harabetian E. Rarefaction and large time behavior for parabolic equations and monotone schemes. Comm Math Phys, 1988, 114: 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--86 [7] Il'in A M, Oleinik O A. Behavior of the solution of the Cauchy problem for certain quasilinear equations for unbounded increase of the time. Amer Math Soc Transl, 1964, 42: 19--23 [8] Ito K. Asymptotic decay toward the planar rarefaction waves of solutions for viscous conservation laws in several dimensions. Math Models Methods Appl Sci, 1996, 6: 315--338 [9] Kawashima S, Nishibata S, Nishikama M. Asymptotic stability of stationary waves for two-dimensional viscous conservation laws in half plane. Discrete and Continuous Dynamical Systems, Supplement, 2003: 469--476 [10] Kawashima S, Nishibata S, Nishikama M. Lp energy method of multi-dimensional viscous conservation laws and application to the stability of planar waves. J Hyperbolic Differential Equations, 2004, 1: 581--603 [11] Liu T P, Matsumura A, Nishihara K. Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves. SIAM J Math Anal, 1998, 29: 293--308 [12] Majda A. Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. New York: Springer-Verlag, 1984 [13] Matsumara A, Nishihara K. Global stability of rarefaction waves of a one-dimension model system for compressible viscous gas. Comm Math Phys, 1992, 144: 325--335 [14] Nakamura T. Asyptotic decay toward the rarefaction waves of solutions for viscous conservation laws in a one-dimensional half space. SIAM J Math Anal, 2003, 34: 1308--1317 [15] Nishikawa M, Nishihara K. Asymptotics toward the planar rarefaction wave for viscous conservation law in two space dimensions. Trans Amer Math Soc, 2000, 352: 1203--1215 [16] Szepessy A, Zumbrun K. Stability of rarefaction waves in viscous media. Arch Rational Mech Anal, 1996, 133(3): 249--298 [17] Wang J H, Zhang H. Existence and decay rates of smooth solutions for a non-uniformly parabolic equation. Proc Roy Soc Edinburgh, Sect A, 2002, 132: 1477--1491 [18] Xin Z P. Asymptotic stability of planar rarefaction waves for viscous conservation laws in several dimensions. Trans Amer Math Soc, 1990, 319: 805--820 [19] Xin Z P. Asymptotic stability of rarefaction waves for 2×2 viscous hyperbolic conservation laws - the two modes case. J Differential Equations, 1989, 78: 191--219 [20] Xu Y L, Jiang M N. Asymptotic stability of rarefaction wave for generalized Burgers equation. Acta Math Sci, 2005, 25B: 119--129 [21] Zhang H. Existence of weak solutions for a degenerate generalized Burgers equation with large initial data. Acta Math Sci, 2002, 22B: 241--248 [22] Zhao H J. Nonlinear stability of strong planar rarefaction waves for the relaxation approximation of conservation laws in several [23] Zhu C J. Asymptotic behavior of solutions for p-system with relaxation. J Differential Equations, 2002, 180: 273--306
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