Geng Di, Qu Chang-zheng. On Nonlinear Hyperbolic Equation in Unbounded Domain[J]. Applied Mathematics and Mechanics, 1992, 13(3): 237-243.
Citation: Geng Di, Qu Chang-zheng. On Nonlinear Hyperbolic Equation in Unbounded Domain[J]. Applied Mathematics and Mechanics, 1992, 13(3): 237-243.

On Nonlinear Hyperbolic Equation in Unbounded Domain

  • Received Date: 1990-11-10
  • Publish Date: 1992-03-15
  • The following nonlinear hyperbolic equation is discussed in this paper:utt+A2u+M(x,||A1/2u||22)Au=0, where A=-Δ+I and x∈Rn. The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local solution of the above equation as M depends on x.
  • loading
  • [1]
    Woinowsky-Krieger, S., The effect of axial force on the vibration of hinged bars, J. Appl. Mech., 17 (1950), 35-36.
    [2]
    Medeiros, L. A., On a new class of nonlinear wave equation, J. Math. Appl., 69(1979),252-262.
    [3]
    Menzala, G. P., On global classical solutions of a nonlinear wave equation, J. Appl. Anal., 10 (1980), 179-195.
    [4]
    Biler, P., Remark on the decay for damped string and beam, Nonlinear Analysis, 10 (1986), 839-842.
    [5]
    Brito, E. H., Decay estimates for generalized damped extensible string and beam equation, Nonlinear Analysis, 8(1984),1489-1496.
    [6]
    Brito, E. H., Nonlinear initial-boundary value problems, Nonlinear Analysis, 11 (1987), 125-137.
    [7]
    Pereira, D. C., Exitence, uniqueness and asymptotic behavior for solutions of the nonlinear beam equation, Nonlinear Analysis, 14 (1990), 613-623.
    [8]
    Vasconcellos, C. F.,On a nonlinear wave equation in unbounded domains, Internat. J. Math. & Math. Sci., 11, 2 (1988), 335-342.
    [9]
    Goldstein, J., Time dependent hyperbolic equation, J. Func. Anal., 4 (1969), 31-49.
  • 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 (2043) PDF downloads(491) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return