Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 633 - 645, Volume 12, Issue 3, October 2009      doi:10.3934/dcdsb.2009.12.633

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Shuyin Wu - School of Mathematics,Yunnan Normal University, 650092 Kunming, China (email)
Joachim Escher - Institute for Applied Mathematics, Leibniz University of Hanover, D-30167 Hanover, Germany (email)
Zhaoyang Yin - Department of Mathematics, Sun Yat-sen University, 510275 Guangzhou, China (email)

Abstract: 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].

Keywords:  Weakly dissipative Degasperis-Procesi equation; Global existence; Blow-up.
Mathematics Subject Classification:  35G25, 35L05.

Received: May 2009;      Revised: June 2009;      Available Online: July 2009.