Title: Global existence and blow-up phenomena for the peakon $b$-family of equations

Authors: Guilong Gui, Yue Liu and Lixin Tian

Issue: Volume 57 (2008), Issue 3, 1209-1234

Abstract: We establish the local well-posedness for the peakon $b$-family of equations which includes both the Camassa-Holm equation and Degasperis-Procesi equation as special cases. We show that the blow-up phenomena occur in finite time for certain initial profiles. Moreover, we obtain a global existence result.