GAN Zai-hui, ZHANG Jian. Global Solution for a Coupled Nonlinear Klein-Gordon System[J]. Applied Mathematics and Mechanics, 2007, 28(5): 603-613.
Citation: GAN Zai-hui, ZHANG Jian. Global Solution for a Coupled Nonlinear Klein-Gordon System[J]. Applied Mathematics and Mechanics, 2007, 28(5): 603-613.

Global Solution for a Coupled Nonlinear Klein-Gordon System

  • Received Date: 2006-04-04
  • Rev Recd Date: 2007-03-09
  • Publish Date: 2007-05-15
  • The global solution for a coupled nonlinear Klein-Gordon system in two space dimensions is studied.First,a sharp threshold of blowup and global existence for the system is obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow.Then the result of how small the initial data are for which the solution of the system exists globally is proved by using the scaling argument.
  • loading
  • [1]
    Guo B L,Yuan G W. Global smooth solution for the Klein-Gordon-Zakharov equations[J].J Math Phys,1995,36(8):4119-4124. doi: 10.1063/1.530950
    [2]
    Bachelot A.Problème de Cauchy globale pour des systèmes de Dirac-klein-Gordon[J].Ann Inst H Poincaré, Physique Théorique,1988,48(4):387-422.
    [3]
    Georgiev V.Global solution of the system of wave and Klein-Gordon equations[J].Math Z,1990,203(4):683-698. doi: 10.1007/BF02570764
    [4]
    Georgiev V.Small amplitude solutions of the Maxwell-Dirac equations[J].Indiana Univ Math J,1991,40(3):845-883. doi: 10.1512/iumj.1991.40.40038
    [5]
    Georgiev V. Decay estimates for the Klein-Gordon equations[J].Comm Part Diff Eqns,1992,17:1111-1139.
    [6]
    Zhang J.On the standing wave in coupled nonlinear Klein-Gordon equations[J].Math Meth Appl Sci,2003,26(1):11-25. doi: 10.1002/mma.340
    [7]
    Segal I.Nonlinear semigroups[J].Annals of Mathematics,1963,78(2):339-364. doi: 10.2307/1970347
    [8]
    Klainerman S. The null condition and global existence to nonlinear wave equations[J].Lect Appl Math,1986,23:293-326.
    [9]
    Klainerman S. Uniform decay estimates and the Lorentz invariance of the classical wave equations[J].Comm Pure Appl Math,1985,38(3):321-332. doi: 10.1002/cpa.3160380305
    [10]
    Ozawa T, Tsutaya K,Tsutsumi Y.Normal formal form and global solutions for the Klein-Gordon-Zakharov equations[J].Annales de I'Institut Henri Poincaré,1995,12(4):459-503.
    [11]
    Shatah J. Normal forms and quadratic nonlinear Klein-Gordon equations[J].Comm Pure Appl Math,1985,38(5):685-696. doi: 10.1002/cpa.3160380516
    [12]
    Sideris T.Decay estimates for the three-dimensional inhomogeneous Klein-Gordon equation and applications[J].Comm Part Diff Eqns,1989,14(10):1421-1455. doi: 10.1080/03605308908820660
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2513) PDF downloads(791) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return