Advertisement

Applied Mathematics and Mechanics

, Volume 24, Issue 6, pp 673–683 | Cite as

Existence of time periodic solutions for a damped generalized coupled nonlinear wave equations

  • Fang Shao-mei
  • Guo Bo-ling
Article

Abstract

The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.

Key words

nonlinear wave equations priori estimate time periodic solution 

Chinese Library Classification

O175.25 O175.29 

2000 MR Subject Classification

35B10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    GUO Bo-ling, TAN Shao-bin. Global smooth solution for a coupled nonlinear wave equations[J].Math Method Appl Sci, 1991,14 (6): 419–425.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Ito M. Symmetries and conservation laws of a coupled nonlinear wave equation[J].Phys Lett A, 1982,91 (7): 335–338.MathSciNetCrossRefGoogle Scholar
  3. [3]
    He P F. Global solutions for a coupled KdV system[J].J Partial Differential Equations, 1989,2 (1): 16–30.MATHMathSciNetGoogle Scholar
  4. [4]
    Hirota R, Satsuma J. Soliton solutions for a coupled KdV equation[J].Phys Lett A, 1981,85 (8/9): 407–421.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Schonbek M E. Existence of solution for the boussinesq system of equation[J].J Differential Equations, 1981,42 (3): 325–352.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Banjamin T B.Lectures in Applied Mathematics[M]. Providence, R I: American Mathematical Society, 1974.Google Scholar
  7. [7]
    GUO Bo-ling. Finite dimensional behavior for weakly damped generalized KdV-Burgers equations[J].Northeast Math J, 1994,10 (3): 309–319.MathSciNetGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Fang Shao-mei
    • 1
    • 2
  • Guo Bo-ling
    • 3
  1. 1.Department of MathematicsShaoguan UniversityShaoguan, GuangdongP. R. China
  2. 2.Graduate SchoolChina Academy of Engineering PhysicsBeijingP. R. China
  3. 3.Institute of Applied Physics and Computational MathematicsBeijingP. R. China

Personalised recommendations