# American Institute of Mathematical Sciences

October  2009, 12(3): 633-645. doi: 10.3934/dcdsb.2009.12.633

## Global existence and blow-up phenomena for a weakly dissipative Degasperis-Procesi equation

 1 School of Mathematics,Yunnan Normal University, 650092 Kunming, China 2 Institute for Applied Mathematics, Leibniz University of Hanover, D-30167 Hanover 3 Department of Mathematics, Sun Yat-sen University, 510275 Guangzhou

Received  May 2009 Revised  June 2009 Published  July 2009

This paper is concerned with the long time behaviour of a weakly dissipative Degasperis-Procesi equation. Our analysis discloses the co-existence of global in time solutions and finite time break down of strong solutions. Our blow-up criterion for the initial profile generalizes considerably results obtained earlier in [32].
Citation: Shuyin Wu, Joachim Escher, Zhaoyang Yin. Global existence and blow-up phenomena for a weakly dissipative Degasperis-Procesi equation. Discrete & Continuous Dynamical Systems - B, 2009, 12 (3) : 633-645. doi: 10.3934/dcdsb.2009.12.633
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