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

Shuyin Wu; Joachim Escher; Zhaoyang Yin

doi:10.3934/dcdsb.2009.12.633

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2009, Volume 12, Issue 3: 633-645. Doi: 10.3934/dcdsb.2009.12.633

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

1.
School of Mathematics,Yunnan Normal University, 650092 Kunming
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: May 2009

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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.

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

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