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半线性摄动电报方程的渐近理论及应用

赖绍永

赖绍永. 半线性摄动电报方程的渐近理论及应用[J]. 应用数学和力学, 1997, 18(7): 611-616.
引用本文: 赖绍永. 半线性摄动电报方程的渐近理论及应用[J]. 应用数学和力学, 1997, 18(7): 611-616.
Lai Shaoyong. The Asymptoic Theory of Semilinear Perturbed Telegraph Equation and Its Application[J]. Applied Mathematics and Mechanics, 1997, 18(7): 611-616.
Citation: Lai Shaoyong. The Asymptoic Theory of Semilinear Perturbed Telegraph Equation and Its Application[J]. Applied Mathematics and Mechanics, 1997, 18(7): 611-616.

半线性摄动电报方程的渐近理论及应用

The Asymptoic Theory of Semilinear Perturbed Telegraph Equation and Its Application

  • 摘要: 对二阶半线性摄动电报方程的初值问题.本交给出了一个渐近方法.证明了渐近理论及形式近似解的合理性都在时间变量无穷大时(即0≤t≤O(|ε|-1)成立.作为浙近理论的应用,我们对一个带初问题的特殊电报方程进行了研究,得到了两个|ε|-1阶渐近近似解.
  • [1] Lu Yuguang,Existence and asymptotic behavior of solution to in homogeneous systems of gas dynamics with viscosity,Acta Mothernatica Scientia,12(1) (1992),51-61.
    [2] 陆云光,非均质系统气体动力学解的渐近性质,科学通报,3(1989),631.
    [3] O,M.Kiselev,Asymptotic solutions of the Cauchy problem of the perturbed Klein-Fock-Gordon equation,Zap,Nauchn,Sem,Leningrad Otdel.Mat.Inst.Stekolw,(LOMI) 16(1987); Mat,Vopr.Teor,R asprostranen 1(1987),115-121(in Russian).
    [4] A.H.J.Cloot and B.M.Herbst,Analytical instability of the Klein Gordobn equation,J.Comput,Appl.Math.,21 (1988),17-26.
    [5] C.G.A,Van Dar Beek,Normal forms for weaky ninlinear perturbed wave equations,Ph.D Thesis,Delft University of Technology,The Netherlands(1989).
    [6] A,L,Shtaras,The averaging method for weakly nonlinear operator equations,Ma t.Sb.,134(2) (1987); Mat.Sb.,62(1) (1987),223-242,(English translation).
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出版历程
  • 收稿日期:  1997-01-20
  • 刊出日期:  1997-07-15

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