Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (2): 652-662.doi: 10.1016/S0252-9602(12)60046-0

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UNIQUE CONTINUATION AND PERSISTENCE PROPERTIES OF SOLUTIONS OF THE 2-COMPONENT DEGASPERIS-PROCESI#br# EQUATIONS

 FU Ying, QU Chang-Zheng   

  1. Department of Mathematics, Northwest University, Xi’an 710069, China;Center for Nonlinear Studies, Northwest University, Xi’an 710069, China
  • Received:2009-11-13 Revised:2010-11-15 Online:2012-03-20 Published:2012-03-20
  • Supported by:

    This work was supported by NNSFC (11001219, 10925104) and the Scientific Research Program Funded by Shaanxi Provincial Education Department (2010JK860).

Abstract:

In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially
together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time.

Key words: 2-component Degasperis-Procesi equation, unique continuation property, persistence property

CLC Number: 

  • 35B30
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