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Communications in Mathematical Physics

, Volume 267, Issue 3, pp 801–820 | Cite as

Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation

  • Yue Liu
  • Zhaoyang YinEmail author
Article

Abstract

This paper is concerned with several aspects of the existence of global solutions and the formation of singularities for the Degasperis-Procesi equation on the line. Global strong solutions to the equation are determined for a class of initial profiles. On the other hand, it is shown that the first blow-up can occur only in the form of wave-breaking. A new wave-breaking mechanism for solutions is described in detail and two results of blow-up solutions with certain initial profiles are established.

Keywords

Soliton Global Existence Travel Wave Solution Wave Breaking Shallow Water Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TexasArlingtonUSA
  2. 2.Department of MathematicsZhongshan UniversityGuangzhouChina
  3. 3.Institute for Applied MathematicsUniversity of HanoverHanoverGermany

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