Abstract
In this paper, we mainly study several problems on the weakly dissipative periodic Camassa-Holm type equation with quadratic and cubic non-linearities. First, in the periodic setting, the local well-posedness of solutions in the Sobolev space is established via Kato's theory. Then, we establish a relation between the behavior of ux and wave breaking phenomena of solutions, and give a sufficient condition on the initial data to guarantee the occurrence of wave breaking. Finally, we obtain the global existence of solutions.
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