A new blow-up criterion for the <i>N</i> – <i>abc</i> family of Camassa-Holm type equation with both dissipation and dispersion
Zaiyun Zhang, Limei Li, Chunhua Fang, Fan He, Chuangxia Huang, Wen Zhu
Abstract
Abstract In this paper, we investigate the Cauchy problem for the N – abc family of Camassa-Holm type equation with both dissipation and dispersion. Furthermore, we establish the blow-up result of the positive solutions in finite time under certain conditions on the initial datum. This result complements the early one in the literature, such as [E. Novruzov, Blow - up phenomena for the weakly dissipative Dullin - Gottwald - Holm equation , J. Math. Phys. 54 (2013), no. 9, 092703, DOI 10.1063/1.4820786] and [Z.Y. Zhang, J.H. Huang, and M.B. Sun, Blow - up phenomena for the weakly dissipative Dullin - Gottwald - Holm equation revisited , J. Math. Phys. 56 (2015), no. 9, 092701, DOI 10.1063/1.4930198].