Acta mathematica scientia,Series A ›› 2003, Vol. 23 ›› Issue (6): 758-768.

• Articles • Previous Articles    

Potential Well Method for a Class of Nonlinear Wave Equations of FourthOrder 

 ZHANG Hong-Wei, CHEN Guo-Wang   

  1. 郑州工程学院数理系 郑州 450052 郑州大学数学系 郑州 4 50052
  • Online:2003-12-25 Published:2003-12-25
  • Supported by:

    国家自然科学基金(10071074)和河南省自然科学基金资助项目

Abstract:

 In this paper the initial boundary value problem for the nonlinear wave equation u_{tt}+u_{xxxx}=σ(u_x)_x+f(x,t)  is  considered.  The existence  of  global  weak  solution  is  proved.  Also  the existence and uniqueness of the  generalized  global  solution  and  the classical global solution are proved.

Key words: Nonlinear wave equation of fourth order;Initial boundary value problem;Exis tence of global solution;Potential well method

CLC Number: 

  • 35L35
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