Abstract
Considered herein is the initial-value problem for the gen eralized periodic Camassa-Holm equation which is related to the Camassa-Holm equation and the Hunter- Saxton equation. Sufficient conditions guaranteeing the de velopment of breaking waves in finite time are demonstrated. On the other hand, the existenc e of strong permanent waves is established with certain initial profiles depending on th e linear dispersive parameter in a range of the Sobolev spaces. Moreover, the admissible global weak solution in the energy space is obtained.
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