Well-posedness and blow-up solution for a modified two-component periodic Camassa-Holm system with peakons. (English) Zbl 1207.35074
The Camassa-Holm equation \(u_{t}-u_{xxt}+3uu_{x}=2u_{x}u_{xx}+uu_{xxx}\) has attracted attention of many authors. Here the modified two-component periodic Camassa-Holm system is considered. For this system the authors have established the local well-posedness and low regularity results of solutions and with description of the precise blow-up scenarios of strong solutions. Also several results of blow-up phenomena with certain initial profiles are detail described with the obtaining the exact blow-up rate.
Reviewer: Svetlana A. Grishina (Ulyanovsk)
MSC:
| 35B44 | Blow-up in context of PDEs |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 35G25 | Initial value problems for nonlinear higher-order PDEs |
| 35B10 | Periodic solutions to PDEs |
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