ON THE UNIQUENESS AND LARGE TIME BEHAVIOR OF THE WEAK SOLUTIONS TO A SHALLOW WATER EQUATION

By Zhouping Xin, Ping Zhang. 2002

148 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b72b059c8769c142b97539a3f2edf300bb1a6284

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation (2010, background): “It is worthwhile to mention that Xin and Zhang [44] proved that the global existence of the weak solution in the energy space H1(R) without any sign conditions on the initial value, and the uniqueness of this weak solution is obtained under some assumptions on the solution [45].”
On Well-Posedness Results for Camassa-Holm Equation on the Line: A Survey (2004, background): “However, in [29], Xin and Zhang proved that if one has a better temporal integrability on ‖∂xu‖L∞ that the one given by (5.”
Global weak solutions and blow-up structure for the Degasperis–Procesi equation (2006, background): “On the other hand, it has global weak solutions in H 1(R) [2,12,15,47,49,50].”
Local well‐posedness and blow‐up criteria of solutions for a rod equation (2005, background): “On the other hand, one can establish like in [19, 20] the well-posedness of weak solutions for the problem (1.”
Global conservative solutions of the generalized hyperelastic-rod wave equation ✩ (2007, result): “2 HOLDEN AND RAYNAUD which was recently studied by Coclite, Holden, and Karlsen [6, 7], extending earlier results for the Camassa–Holm equation by Xin and Zhang, see [20].”
Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View (2007, methodology): “Global dissipative solutions of a more general class of equations were recently derived by Coclite et al. (2005a,b), improving upon Xin and Zhang (2000, 2002).”
On the well-posedness of the Degasperis-Procesi equation (2006, background): “Existence and uniqueness results for global weak solutions of the Camassa–Holm equation are proved in [4,9,12,34,35,15,16].”
A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation (2006, background): “Xin, Z., Zhang, P. (2002).”
On the blow-up of solutions to the integrable modified Camassa–Holm equation (2014, background): “The existence of global weak solutions was investigated in [25, 26].”
Dissipative solutions for the Camassa-Holm equation (2009, methodology): “Global dissipative solutions of a more general class of equations were derived by Coclite, Holden, and Karlsen [7, 8], improving upon [25, 26].”
WELL-POSEDNESS OF HIGHER-ORDER CAMASSA-HOLM EQUATIONS (2009, result): “A similar result was proved in [30], in the case k = 1, for the Camassa–Holm equation.”