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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (3): 391-401.doi: https://doi.org/10.1007/s10483-009-0313-x

• Articles • 上一篇    

Initial value problem for a class of fourth-order nonlinear wave equations

陈国旺,侯长顺   

  1. 1. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P. R. China;
    2. College of Mathematics and Physics, Henan University of Technology, Zhengzhou 450052, P. R. China
  • 收稿日期:2008-02-11 修回日期:2009-01-16 出版日期:2009-03-05 发布日期:2009-03-01
  • 通讯作者: Guo-wang CHEN, Professor, Ph. D., E-mail: chenguowang@zzu.edu.cn E-mail:chenguowang@zzu.edu.cn

Initial value problem for a class of fourth-order nonlinear wave equations

Guo-wang CHEN, Chang-shun HOU   

  1. 1. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P. R. China;
    2. College of Mathematics and Physics, Henan University of Technology, Zhengzhou 450052, P. R. China
  • Received:2008-02-11 Revised:2009-01-16 Online:2009-03-05 Published:2009-03-01
  • Contact: Guo-wang CHEN, Professor, Ph. D., E-mail: chenguowang@zzu.edu.cn E-mail:chenguowang@zzu.edu.cn

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摘要： In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.

关键词: fourth-order nonlinear wave equation, initial value problem, global solution, blow up of solution

Abstract: In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.

Key words: fourth-order nonlinear wave equation, initial value problem, global solution, blow up of solution

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