Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (6): 1461-1469.

• Articles •     Next Articles

Study on a Free Boundary Value Problem Arising from Peeling Phenomenon

 ZHAO Wei-Xia   

  1. School of Mathematical Science, Fudan University, Shanghai 200433
  • Received:2009-10-15 Revised:2011-09-10 Online:2011-12-25 Published:2011-12-25
  • Supported by:

    国家自然科学基金重点项目(11031001)和国家教育部博士点基金(20090071110002)资助.

Abstract:

In this paper the following free boundary problem
{utt-∂x(ux/√1+ux2)=0,    in{(t, x)|t>0, x>-l0}∩{u>0},

1/2ut2+1/√1+ux2-1+Q=0,   in{(t, x)|t>0, x>-l0}∩∂{u>0}
 is considered. The problem describes the peeling phenomenon. Different from the problem studied by K. Kikuchi and S. Omata,  the nonlinear effects in the vibrating string is also considered. Under some reasonable assumptions, the local existence and uniqueness of classical solution for the free boundary problem is proved.

Key words: Peeling phenomenon, Free boundary value problem, Nonlinear vibrating string equation

CLC Number: 

  • 35L70
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