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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Zhengzhou University, Zhengzhou, 450052, P. R. China

    Guo-wang Chen  (陈国旺)

  2. College of Mathematics and Physics, Henan University of Technology, Zhengzhou, 450052, P. R. China

    Chang-shun Hou  (侯长顺)

Authors
  1. Guo-wang Chen  (陈国旺)
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  2. Chang-shun Hou  (侯长顺)
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Corresponding author

Correspondence to Guo-wang Chen  (陈国旺).

Additional information

(Communicated by Shi-qiang DAI)

Project supported by the National Natural Science Foundation of China (No. 10671182)

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Chen, Gw., Hou, Cs. Initial value problem for a class of fourth-order nonlinear wave equations. Appl. Math. Mech.-Engl. Ed. 30, 391–401 (2009). https://doi.org/10.1007/s10483-009-0313-x

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  • DOI: https://doi.org/10.1007/s10483-009-0313-x

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2000 Mathematics Subject Classification

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