GAN Zai-Hui, ZHANG Jian. Asymptotic Theory of Initial Value Problems for Nonlinear Perturbed Klein-Gordon Equations[J]. Applied Mathematics and Mechanics, 2005, 26(7): 833-839.
Citation: GAN Zai-Hui, ZHANG Jian. Asymptotic Theory of Initial Value Problems for Nonlinear Perturbed Klein-Gordon Equations[J]. Applied Mathematics and Mechanics, 2005, 26(7): 833-839.

Asymptotic Theory of Initial Value Problems for Nonlinear Perturbed Klein-Gordon Equations

  • Received Date: 2003-03-07
  • Rev Recd Date: 2005-04-26
  • Publish Date: 2005-07-15
  • 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.
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