Global existence and propagation speed for a generalized Camassa–Holm model with both dissipation and dispersion

[1]  I. Sibgatullin.  well-posedness , 2020 .

[2]  Chen Wang,et al.  BLOW-UP , 2016, ACM Trans. Sens. Networks.

[3]  E. Novruzov,et al.  On the behavior of the solution of the dissipative Camassa–Holm equation with the arbitrary dispersion coefficient , 2014 .

[4]  A. Alexandrou Himonas,et al.  Persistence properties and unique continuation for a generalized Camassa-Holm equation , 2014 .

[5]  A. Himonas,et al.  Norm Inflation and Ill-Posedness for the Degasperis-Procesi Equation , 2014 .

[6]  A. Himonas,et al.  The Cauchy problem for a generalized Camassa-Holm equation , 2014, Advances in Differential Equations.

[7]  Chunlai Mu,et al.  Well-posedness, blow-up phenomena and global existence for thegeneralized $b$-equation with higher-order nonlinearities and weak dissipation , 2013 .

[8]  Chunlai Mu,et al.  The Properties of Solutions for a Generalized b-Family Equation with Peakons , 2013, J. Nonlinear Sci..

[9]  Yongsheng Li,et al.  The Cauchy problem for the Novikov equation , 2012, Nonlinear Differential Equations and Applications NoDEA.

[10]  Qiaoyi Hu.  Global existence and blow-up phenomena for a weakly dissipative periodic 2-component Camassa-Holm system , 2011 .

[11]  Z. Yin,et al.  Global weak solutions for the Novikov equation , 2011 .

[12]  Feride Tiglay,et al.  The periodic Cauchy problem for Novikov's equation , 2010, 1009.1820.

[13]  Vladimir S. Novikov,et al.  Generalizations of the Camassa–Holm equation , 2009 .

[14]  Z. Yin,et al.  Blowup and blowup rate of solutions to a weakly dissipative periodic rod equation , 2009 .

[15]  H. Holden,et al.  Dissipative solutions for the Camassa-Holm equation , 2009 .

[16]  H. Holden,et al.  WELL-POSEDNESS OF HIGHER-ORDER CAMASSA-HOLM EQUATIONS , 2009 .

[17]  Jing Ping Wang,et al.  Integrable peakon equations with cubic nonlinearity , 2008, 0805.4310.

[18]  Zhaoyang Yin,et al.  Blow-Up and Decay of the Solution of the Weakly Dissipative Degasperis-Procesi Equation , 2008, SIAM J. Math. Anal..

[19]  H. Holden,et al.  Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View , 2007 .

[20]  A. Bressan,et al.  Global Conservative Solutions of the Camassa–Holm Equation , 2007 .

[21]  Giuseppe Maria Coclite,et al.  On the well-posedness of the Degasperis-Procesi equation , 2006 .

[22]  Dai Hui-hui,et al.  On the Cauchy Problem of the Camassa-Holm Equation , 2006 .

[23]  Zhaoyang Yin,et al.  Blow-up, blow-up rate and decay of the solution of the weakly dissipative Camassa-Holm equation , 2006 .

[24]  Zhaoyang Yin,et al.  Global existence for a new periodic integrable equation , 2003 .

[25]  Zhaoyang Yin,et al.  On the Cauchy problem for an integrable equation with peakon solutions , 2003 .

[26]  Darryl D. Holm,et al.  A New Integrable Equation with Peakon Solutions , 2002, nlin/0205023.

[27]  Darryl D. Holm,et al.  The Camassa-Holm hierarchy, related N-dimensional integrable systems, and algebro-geometric solution on a symplectic submanifold , 2002, nlin/0202009.

[28]  A. Constantin,et al.  The initial value problem for a generalized Boussinesq equation , 2002, Differential and Integral Equations.

[29]  Ping Zhang,et al.  On the weak solutions to a shallow water equation , 2000 .

[30]  Adrian Constantin,et al.  On the Blow-Up of Solutions of a Periodic Shallow Water Equation , 2000, J. Nonlinear Sci..

[31]  P. Olver,et al.  Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation , 2000 .

[32]  J. Escher,et al.  On the structure of a family of quasilinear equations arising in shallow water theory , 1998 .

[33]  J. Escher,et al.  Wave breaking for nonlinear nonlocal shallow water equations , 1998 .

[34]  J. Escher,et al.  Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation , 1998 .

[35]  A. Constantin.  On the Cauchy Problem for the Periodic Camassa–Holm Equation , 1997 .

[36]  P. Olver,et al.  Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[37]  A. Fokas.  On a class of physically important integrable equations , 1994 .

[38]  Darryl D. Holm,et al.  An integrable shallow water equation with peaked solitons. , 1993, Physical review letters.

[39]  J. Ghidaglia.  Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time , 1988 .

[40]  Athanassios S. Fokas,et al.  Symplectic structures, their B?acklund transformation and hereditary symmetries , 1981 .

[41]  E. Ott,et al.  Damping of Solitary Waves , 1970 .

[42]  H. P. MCKEANt.  BREAKDOWN OF A SHALLOW WATER EQUATION* , 2016 .

[43]  Z. Yin,et al.  Well-posedness and global existence for the Novikov equation , 2012 .

[44]  A. Bressan,et al.  GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION , 2007 .

[45]  Joachim Escher,et al.  Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation , 2007 .

[46]  A. Constantin.  Existence of permanent and breaking waves for a shallow water equation: a geometric approach , 2000 .

[47]  J. Escher,et al.  Global existence and blow-up for a shallow water equation , 1998 .

[48]  Darryl D. Holm,et al.  A New Integrable Shallow Water Equation , 1994 .