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Open Access Research

Blow-up phenomena and global existence for the weakly dissipative generalized periodic Degasperis-Procesi equation

Caochuan Ma1*, Ahmed Alsaedi2, Tasawar Hayat23 and Yong Zhou24

Author Affiliations

1 Department of Mathematics, Tianshui Normal University, Tianshui, Gansu, 741001, P.R. China

2 Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

3 Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad, 44000, Pakistan

4 Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, P.R. China

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Boundary Value Problems 2014, 2014:123  doi:10.1186/1687-2770-2014-123

Published: 20 May 2014

Abstract

In this paper, we investigate the Cauchy problem of a weakly dissipative generalized periodic Degasperis-Procesi equation. The precise blow-up scenarios of strong solutions to the equation are derived by a direct method. Several new criteria guaranteeing the blow-up of strong solutions are presented. The exact blow-up rates of strong solutions are also determined. Finally, we give a new global existence results to the equation.

MSC: 35G25, 35Q35, 58D05.

Keywords:
weakly dissipative; generalized periodic Degasperis-Procesi equation; blow-up; global existence; blow-up rate