On the Cauchy problem for the periodic b-family of equations and of the non-uniform continuity of Degasperis-Procesi equation

We consider the problem of the existence of the global solutions and formation of singularities for a b-family of equations which includes the Camassa-Holm and Degasperis-Procesi equation. We also consider the problem of the uniformly continuity of Degasperis-Procesi equation. (C) 2009 Elsevier Inc. All rights reserved.