XU Run-zhang, ZHAO Xi-ren, SHEN Ji-hong. Asymptotic Behaviour of Solution for Fourth Order Wave Equation With Dispersive and Dissipative Terms[J]. Applied Mathematics and Mechanics, 2008, 29(2): 235-238.
Citation: XU Run-zhang, ZHAO Xi-ren, SHEN Ji-hong. Asymptotic Behaviour of Solution for Fourth Order Wave Equation With Dispersive and Dissipative Terms[J]. Applied Mathematics and Mechanics, 2008, 29(2): 235-238.

Asymptotic Behaviour of Solution for Fourth Order Wave Equation With Dispersive and Dissipative Terms

  • Received Date: 2007-08-15
  • Rev Recd Date: 2008-01-03
  • Publish Date: 2008-02-15
  • The initial boundary value problem of fourth order wave equation with dispersive and dissipative terms is studied.By using multiplier method,it was proven that the global strong solution of the problem decays to zero exponentially as the time approaches infinite,under a very simple and mild assumption regarding the nonlinear term.
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  • [1]
    Bogolubsky I L.Some examples of inelastic soliton interaction[J].Computer Physics Communications,1977,13(1):149-155. doi: 10.1016/0010-4655(77)90009-1
    [2]
    Clarkson P A, Leveque R J, Saxton R A. Solitary wave interaction in elastic rods[J].Studies in Applied Mathematics,1986,75(1):95-122.
    [3]
    庄蔚,杨桂通.孤波在非线性弹性杆中的传播[J].应用数学和力学,1986,7(7):571-582.
    [4]
    张善元,庄蔚.非线性弹性杆中的应变孤波[J].力学学报,1988,20(1):58-66.
    [5]
    Seyler C E, Fanstermacher D L. A symmetric regularized long wave equation[J].Phys Fluids,1984,27(1):4-7. doi: 10.1063/1.864487
    [6]
    CHEN Guo-wang,YANG Zhi-jian,ZHAO Zhan-cai.Initial value problem and first boundary problem for a class of quasilinear wave equations[J].Acta Math Appl Sinica,1993,9(4):289-301. doi: 10.1007/BF02005918
    [7]
    YANG Zhi-jian. Existence and non-existence of global solutions to a generalized modification of the improved Boussinesq equation[J].Math Mech Appl Sci,1998,21(16):1467-1477. doi: 10.1002/(SICI)1099-1476(19981110)21:16<1467::AID-MMA968>3.0.CO;2-K
    [8]
    GUO Bo-ling. The spectral method for symmetric regularized wave equations[J].J Comp Math,1987,5(4):297-306.
    [9]
    杨志坚,宋长明.关于一类非线性发展方程整体解的存在性问题[J].应用数学学报,1997, 20(3):321-331.
    [10]
    郭柏灵.粘性消动法和差分格式粘性[M].北京:科学出版社,1993.
    [11]
    朱位秋.弹性杆中的非线性波[J].固体力学学报,1980,1(2):247-253.
    [12]
    尚亚东.方程utt-Δu-Δut-Δtt=f(u)的初边值问题[J].应用数学学报,2000,23(3):385-393.
    [13]
    刘亚成,李晓媛.关于方程utt-Δu-Δut-Δtt=f(u)的某些注记[J].黑龙江大学自然科学学报,2004,21(3):1-6.
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