Acta mathematica scientia,Series A ›› 1997, Vol. 17 ›› Issue (2): 121-128.

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Global Exisence of Classical Solution to the Nonlinear Wave Equations

Qin Yuming   

  1. 1 Mathematics Department of Henan University, Kaifeng 475001;
    2 Institute of Mathematics of Fudan University, Shanghai 200433
  • Received:1995-02-20 Revised:1995-07-13 Online:1997-04-26 Published:1997-04-26

Abstract: In this paper the existence and uniqueness of global Classical solution to the cauchy problem for the wave equation to uu-△u=F(u, Du) are proved. Moreover, the decaying esimates of every terms u,Du,D2u appearing in the equation are obtained, which arethe same as the corresponding homogeneous equation. The results of this paper supplementsthe results in[4] where F does not contain u explicitly.

Key words: global solution, Cauchy problem, decaying estimates

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