A new blow-up criterion for the N – abc family of Camassa-Holm type equation with both dissipation and dispersion

Open Mathematics

Huang Chuangxia¹  Zhu Wen²  Li Limei³  He Fan³  Zhang Zaiyun³  Fang Chunhua³ 

[1] Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, and School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410014, Hunan Province, China;Key Laboratory of Data science and Smart Education, Ministry of Education, Hainan Normal University, Haikou, 571158, China;School of Mathematics, Hunan Institute of Science and Technology, Yueyang, 414006, Hunan, China;

关键词: blow-up;    n-abc family of camassa-holm type equation;    dissipation;    dispersion;    35a07;    35q53;   

DOI  :  10.1515/math-2020-0012

来源: DOAJ

【 摘 要 】

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].

【 授权许可】

Unknown