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Applied Mathematics and Mechanics

, Volume 26, Issue 7, pp 907–913 | Cite as

Asymptotic theory of initial value problems for nonlinear perturbed Klein-Gordon equations

  • Gan Zai-hui
  • Zhang Jian
Article
  • 30 Downloads

Abstract

The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered. Firstly, using the contraction mapping principle, combining some priori estimates and the convergence of Bessel function, the well-posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein-Gordon equations. Next, formal approximations of initial value problem was constructed by perturbation method and the asymptotic validity of the formal approximation is got. Finally, an application of the asymptotic theory was given, the asymptotic approximation degree of solutions for the initial value problem of a specific nonlinear Klein-Gordon equation was analyzed by using the asymptotic approximation theorem.

Key words

Klein-Gordon equations well-posedness asymptotic theory formal approximations application 

Chinese Library Classification

O175.29 

2000 Mathematics Subject Classification

35A15 35L15 

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2005

Authors and Affiliations

  1. 1.College of Mathematics and Software ScienceSichuan Normal UniversityChengduP. R. China

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