[1] Camassa R, Holm D D. An integrable shallow water equation with peaked solitons. Phys Rev Lett, 1993,
71(11): 1661–1664
[2] Coclite G M, Holden H, Karlsen K H. Global weak solutions to a generalized hyperelastic-rod wave
equation. E-print, Department of Mathematics, Universtity of Oslo, 2004
[3] Coclite G M, Holden H, Karlsen K H. Wellposedness for a parabolic-elliptic system system. Discrete and
Continuous Dynamical Systems, 2005, 13(3): 659–682
[4] Coclite G M, Karlsen K H. A singular limit problem for conservation laws related to the Camassa-Holm
shallow water equation. Preprint, 2005
[5] Constantin A. Existence of permanent and breaking waves for a shallow water equation: a geometric
approach. Ann Inst. Fourier (Grenoble), 2000, 50(2): 321–362
[6] Constantin A, Escher J. Global existence and blow-up for a shallow water equation. Ann Scuola Norm
Sup Pisa Cl Sci (4), 1998, 26(2): 303–328
[7] Constantin A, Escher J. Global weak solutions for a shallow water equations. Indiana Univ Math J, 1998,
47(4): 1527–1545
[8] Constantin A, Escher J. Wave breaking for nonlinear nonlocal shallow water equations. Acta Math, 1998,
181(2): 229–243
[9] Constantin A, Molinet L. Global weak solutions for a shallow water equation. Comm Math Phys, 2000,
211(1): 45–61
[10] Danchin R. A few remarks on the Camassa-Holm equation. Differential Integral Equations, 2001, 14(8):
953–988
[11] Danchin R. A note on well-posedness for Camassa-Holm equation. J Differential Equations, 2003, 192(2):
429–444
[12] Duan R, Zhao H J. Global stability of strong rarefaction waves for the generalized Kdv-Burgers equation.
Nonlinear Analysis, TMA, 2007, 66: 1100–1117
[13] Duan R, Ma X, Zhao H J. A case study of global stability of strong rarefaction waves for 2×2 hyperbolic
conservation laws with artificial viscosity. J Differential Equations, 2006, 228: 259–284
[14] Hattori Y, Nishihara K. A note on the stability of rarefaction wave of the Burgers equation. Jpn J Indust
Appl Math, 1991, 8: 85–96
[15] Himonas A A, Misiolek G. The Cauchy problem for an integrable shallow-water equation. Differential
Integral Equations, 2001, 14(7): 821–831
[16] Il’in A M, Oleinik O A. Asymptotic behavior of the solutions of Cauchy problem for certain quasilinear
equations for large time (Russian). Mat Sbornik, 1960, 51:191–216
[17] Ito K. Asymptotic decay toward the planar rarefaction waves of solutions for viscous conservation laws in
several space dimensions. Math Models Methods Appl Sci, 1996, 6(3): 315–338
[18] Johnson R S. Camassa-Holm, Kortewey-de Vries and related models for water waves. J Fluid Mech, 2002,
455: 63–82
[19] Li Y A, Olver P J. Well-pesedness and blow-up solutions for an integrable nonlinearly dispersive model
wave equation. J Differential Equations, 2000, 162(1):27–63
[20] Liu T P, Matsumura A, Nishihara K. Behavior of solutions for the Burgers equations with boundary
corresponding to rarefaction waves. SIAMJ Math Mech, 1998, 29: 293–308
[21] Matsumura A, Nishihara K. Asymptotics toward the rarefaction waves of the solutions of a one-dimensional
model system for compressible viscous gas. Jpn J Appl Math, 1986, 3:1–13
[22] Matsumura A, Nishihara K. Global stability of the rarefaction wave of a one-dimensional model system
for compressible viscous gas. Comm Math Phys, 1992, 144: 325–335
[23] Nishihara K. Asymptotic behavior of solutions to viscous conservation laws via the L2-energy method.
Advances in Mathematics, 2001, 30: 293–321
[24] Rodriguez-Blanco G. On the Cauchy problem for the Camassa-Holm equation. Nonlinear Anal, 2001,
46(3, Ser. A:Theory Methods): 309–327
[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):
1411–1433
[27] Xin Z, Zhang P. On the uniqueness and large time behavior of the weak solutions to a shallow water
equation. Comm Patial Differential Equations, 2002, 27(9/10): 1815–1844
[28] Zhao H J. Solutions in the large for certain nonlinear parabolic systems in arbitrary spatial dimensions.
Applicable Analysis, 1995, 59: 349–376
[29] Zhao H J. Decay estimates for the solution of some multidimensional nonlinear evolution equations. Comm
Patial Differential Equations, 2000, 25(3/4): 377–422
[30] Zhao H J. Nonlinear stability of strong planar rarefaction waves for the relaxation approximation of
conservation laws in several sapce dimensions. J Differential Equations, 2000, 163: 192–222
[31] Zhu C J. Asymptotic behavior of solutions for P-system with relaxation. J Differential Equation, 2002,
180: 273–306
[32] Zhu C J, Wang Z A. Decay rates of solutions to dissipative nonlinear evolution equations with ellipticity.
Z Angew Math Phys, 2004, 55: 1–21 |