Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (6): 1523-1536.

• Articles • Previous Articles     Next Articles

On the Unique Continuation Property for a Nonlinear Dispersive System

  

  1. 1.School of Science,Xi'an Jiaotong University, Xi'an 710049;
    2.Department of Mathematics, Northwest University, Xi'an 710069
  • Received:2007-10-29 Revised:2008-11-17 Online:2009-12-25 Published:2009-12-25
  • Supported by:

    国家自然科学基金(10671153; 10671156)资助

Abstract:

It is proved that, if a sufficiently smooth solution $(u,v)=(u(x,t),v(x,t))$ to the initial value problem associated with the dispersive coupled system
{∂ u+∂3x u+∂ x(up vp+1)=0,
 ∂v+∂3x v+∂x(up+1vp)=0,        x ∈R, t ≥ 0
is supported on a half line at two different instants of time then u ≡ 0, v ≡ 0.

Key words: Coupled dispersive system, Compact support, Unique continuation property

CLC Number: 

  • 35B30
Trendmd