Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (2): 371-390.doi: 10.1016/S0252-9602(09)60037-0
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Ma Xuan|Yin Hui|Jing Jin
Received:
2006-09-30
Online:
2009-03-20
Published:
2009-03-20
Contact:
Yin Hui
E-mail:yinhui928@126.com
Supported by:
This work was supported by two grants from the National Natural Science Foundation of China under contracts 10431060 and 10329101, respectively
Ma Xuan|Yin Hui|Jing Jin. GLOBAL ASYMPTOTICS TOWARD THE REREFACTION WAVES FOR A PARABOLIC-ELLIPTIC SYSTEM RELATED TO THE CAMASSA-HOLM SHALLOW WATER EQUATION[J].Acta mathematica scientia,Series B, 2009, 29(2): 371-390.
[14] Hattori Y, Nishihara K. A note on the stability of rarefaction wave of the Burgers equation. Jpn J Indust [15] Himonas A A, Misiolek G. The Cauchy problem for an integrable shallow-water equation. Differential [16] Il’in A M, Oleinik O A. Asymptotic behavior of the solutions of Cauchy problem for certain quasilinear [17] Ito K. Asymptotic decay toward the planar rarefaction waves of solutions for viscous conservation laws in [18] Johnson R S. Camassa-Holm, Kortewey-de Vries and related models for water waves. J Fluid Mech, 2002, [19] Li Y A, Olver P J. Well-pesedness and blow-up solutions for an integrable nonlinearly dispersive model [20] Liu T P, Matsumura A, Nishihara K. Behavior of solutions for the Burgers equations with boundary [21] Matsumura A, Nishihara K. Asymptotics toward the rarefaction waves of the solutions of a one-dimensional [22] Matsumura A, Nishihara K. Global stability of the rarefaction wave of a one-dimensional model system [23] Nishihara K. Asymptotic behavior of solutions to viscous conservation laws via the L2-energy method. [24] Rodriguez-Blanco G. On the Cauchy problem for the Camassa-Holm equation. Nonlinear Anal, 2001, [25] Smoller J. Shock waves and reaction-diffusion equations. New York-Berlin: Springer-Verlag, 1983 [26] Xin Z, Zhang P. On the weak solutions to a shallow water equation. Comm Pure Appl Math, 2000, 53(11): [27] Xin Z, Zhang P. On the uniqueness and large time behavior of the weak solutions to a shallow water [28] Zhao H J. Solutions in the large for certain nonlinear parabolic systems in arbitrary spatial dimensions. [29] Zhao H J. Decay estimates for the solution of some multidimensional nonlinear evolution equations. Comm [30] Zhao H J. Nonlinear stability of strong planar rarefaction waves for the relaxation approximation of [31] Zhu C J. Asymptotic behavior of solutions for P-system with relaxation. J Differential Equation, 2002, [32] Zhu C J, Wang Z A. Decay rates of solutions to dissipative nonlinear evolution equations with ellipticity. |
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