留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

力学中单参数变换群的应用

许学咨 陈怀永

许学咨, 陈怀永. 力学中单参数变换群的应用[J]. 应用数学和力学, 1990, 11(7): 636-642.
引用本文: 许学咨, 陈怀永. 力学中单参数变换群的应用[J]. 应用数学和力学, 1990, 11(7): 636-642.
Xu Xue-zi, Chen Huai-yong. Application of One-Parameter Groups of Transformation in Mechanics[J]. Applied Mathematics and Mechanics, 1990, 11(7): 636-642.
Citation: Xu Xue-zi, Chen Huai-yong. Application of One-Parameter Groups of Transformation in Mechanics[J]. Applied Mathematics and Mechanics, 1990, 11(7): 636-642.

力学中单参数变换群的应用

Application of One-Parameter Groups of Transformation in Mechanics

  • 摘要: 本文包括无限小形式的变换群用于减少偏微分方程中的自变量,获得相似变量的理论,以及它在力学中具有两个自变量、两个因变量的非线性偏微分方程组中的应用.
  • [1] Birkhoff,G.,Hydrodynamics,2nd Ed,Princeton University Press(1960).
    [2] Michal,A.D.,Differential invariants and invariant partial differential equations under continuous transformation groups in normed linear spaces,Proc.Nat.Acad.Sci.,37(1951),623-627.
    [3] Morgan,A.J.A.,The reduction by one of the number of independent variables in some systems of partial differential equations.Quart.J.Math.,Oxford,Ser.2(1952),250-259.
    [4] Hansen,A.G.,Similarity Analyses of Boundary Value Problems in Engineering,Prentice-Hall(1964).
    [5] Ames,W.F.,Similarity for the nonlinear diffusion equation,Ind.Eng.Chem.Fundam.,4,1(1965),72-76.
    [6] Lee,S.Y.and W.F.Ames,Similarity solutions for non-Newtonian fluids.A.I.Ch.E.J.,12.44(1966),700-708.
    [7] Na,T.Y.and A.G.Hansen,Possible similarity solutions of the laminar natural convection flow of non-Newtonian fluids,Int.J.Heat Mass Transfer,9(1966),261-626.
    [8] Na.Y.T.and A.G.Hansen,Similarity solutions of a class of laminar three-dimensional boundary layer equations of power law fluids,Int.J.Non-Linear Mech.,2(1967),373-385.
    [9] Gabbert,C.H.,Similarity for unsteady compressible boundary layers,AIAA J.,5,6(1967),1198-1200.
    [10] Moran.M.J.and R.A.Gaggioli,Reduction of the number of variables in systems of partial differential equations,with auxiliary conditions,SIAM J.Appl.Math.,16(1968),202-215.
    [11] Hansen,A.G.and T.Y.Na,Similarity solutions of laminar,incompressible boundary layer equations of non-Newtonian fluids,J.Basic Eng(1968),71-74.
    [12] Moran,M.J.and R.A.Gaggioli,Similarity analyses via group theory,AIAA J.,6,10(1968),2014-2016.
    [13] Ames.W.F.,Nonlinear partial differential equations in Engineering.Vol.Ⅱ(1972).
    [14] Bluman,G.W and J.D.Cole,Similarity methods for differential equations,Springer-Verlag.New York(1974).
    [15] Dresner,L.Sanilarity Solutions Nonlinear Partial Differential Equations.Pitman(1983).
    [16] Frydryehowicv,W.and M.C.Singh,Group theoretic and similarity analysis of hyperbolic partial differential equations,J.Math.Anal.Appl.,114(1986),75-99.
    [17] Iimol,M.G.and N.L.Kalthia,Similarity solutions of three-dimensional boundary layer equations of non-Newtonian fluids,Int.J.Nonlinear Mech.,21,6(1986),475-481.
    [18] Donato,A.,Similarity analysis and non-linear wave propagation,Int.J.Non-Linear Mech.,22.4(1987),307-314.
    [19] Bluman,G.W.and J.D.Cole,The general similarity solution of the heat equation,J.Math.Mech.,18,11(1969),1025-1042.
    [20] Nariboli,G.A.Self-similar solutions of some nonlinear equations,Appl.Sci.Res.,22(1970),449-461.
    [21] Bluman,G.W.,Slimlarity solutions of the one-dimensional Fokker-Planck equation,Int.J.Non-Linear Mech.,6(1971),143-153.
    [22] Bluman,G.W.and J.D.Cole,Similarity Methods for Differential Equations,Springer,Berlin(1974).
    [23] Bluman,G.W.Applications of the general similarity solution of the heat equation to boundary-value problems Quart.Appl.Math.,(1974),403-415.
    [24] Shen,H.and W.F.Ames,On invariant solutions of the Korteweg-de Vries equation,Phys.Lett.,49A(1974),313-314.
    [25] Mayer,Humi,Invariant solutions for a class of diffusion equations,J.Math.Phys.,18,6(1977),1705-1708.
    [26] Lakshmanan,M.and P.Kaliappan,On the invariant solutions of the Korteweg-de Vries-Burgers equations.Phys.Lett.,71A,2/3(1979),166-168.
    [27] Seshadri(edmonton),R.and M.C.Singh(calgary),Similarity analysis of wave propagation problems in nonlinear rods,Arch.Mech.,32,b(1980),933-945.
    [28] Logan,J.D.and J.D,J.Perey,Similarity solutions for reactive shock hydrodynamics,SIAM.J.Appl.Math.,39,3(1980),512-527.
    [29] Thien,N.P.,A method to obtain some similarity solutions to the generalized Newtonian fluid,ZAMP,32(1981).609-615.
    [30] Lioyd,S.P.,The infinitesimal group of the Navier-Stokes equations,Acta Mech.,38(1981),85-98.
    [31] Ames,W.F.and R J.Lohner,Group properties of Ua=[ƒ(u)ux]x,Int.J.Non-linear Mech.,16,5/6(1981),439-447.
    [32] Hill.J.M.,Solution of Differential Equations by Means of One-Parameter Group pitman(1982).
    [33] 许学咨、陈怀永.群论在力学中的应用,第一届华东地区流体力学学术会议论文集(二)(1988),283-295.
  • 加载中
计量
  • 文章访问数:  2094
  • HTML全文浏览量:  123
  • PDF下载量:  942
  • 被引次数: 0
出版历程
  • 收稿日期:  1989-08-17
  • 刊出日期:  1990-07-15

目录

    /

    返回文章
    返回