Global existence and blow-up phenomena for the peakon $b$-family of equations Guilong GuiYue LiuLixin Tian 35G2535L05local existenceglobal existenceblow-upCamassa-Holm equationDegasperis-Procesi equationpeakon $b$-family of equations 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. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3213 10.1512/iumj.2008.57.3213 en Indiana Univ. Math. J. 57 (2008) 1209 - 1234 state-of-the-art mathematics http://iumj.org/access/