Article

Applied Mathematics and Mechanics

, Volume 30, Issue 3, pp 391-401

First online:

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

  • Guo-wang Chen陈国旺Affiliated withDepartment of Mathematics, Zhengzhou University Email author 
  • , Chang-shun Hou侯长顺Affiliated withCollege of Mathematics and Physics, Henan University of Technology

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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

Chinese Library Classification

O175.29 O175.27

2000 Mathematics Subject Classification

35L30 35G25