Applied Mathematics and Mechanics

, Volume 30, Issue 3, pp 391–401

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

  • Guo-wang Chen (陈国旺)
  • Chang-shun Hou (侯长顺)
Article

DOI: 10.1007/s10483-009-0313-x

Cite this article as:
Chen, G. & Hou, C. Appl. Math. Mech.-Engl. Ed. (2009) 30: 391. doi:10.1007/s10483-009-0313-x

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 equationinitial value problemglobal solutionblow up of solution

Chinese Library Classification

O175.29O175.27

2000 Mathematics Subject Classification

35L3035G25

Copyright information

© Shanghai University and Springer-Verlag GmbH 2009

Authors and Affiliations

  • Guo-wang Chen (陈国旺)
    • 1
  • Chang-shun Hou (侯长顺)
    • 2
  1. 1.Department of MathematicsZhengzhou UniversityZhengzhouP. R. China
  2. 2.College of Mathematics and PhysicsHenan University of TechnologyZhengzhouP. R. China