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

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