Similarity Analysis of Boundary Value Problems with Finite Boundaries

  • R. Seshadri
  • T. Y. Na


It is commonly believed that similarity analysis of boundary value problems in science and engineering is domain-and-boundary condition limited, in that semi-infinite or infinite domains are required. A review of literature on similarity would, indeed, reveal that similarity solutions are mostly available for boundary value problems that lack a characteristic length in one or more coordinate directions. In his book, Hansen 1 points out that problems with finite boundaries associated with finite, non-zero values do not usually possess similarity solutions. Therefore, he suggests that a lack of characteristic length in a coordinate direction could be used as a hint to proceed with similarity analysis and seek possible solutions.


Similarity Solution Auxiliary Condition Finite Domain Affine Group Infinite Domain 
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  1. 1.
    Hansen A.G., Similarity Analysis of Boundary Value Problems in Engineering, Princeton Hall (1960).Google Scholar
  2. 2.
    Carslaw H.S. and Jaeger J.C., Conduction of Heat in Solids, 2nd edition,Oxford Univ. Press,London (1959).Google Scholar
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    Bluman G.W., “Applications of the General Similarity Solution of the Heat Equation to Boundary Value Problems”, Quar. Appl. Math., Vol. 31, No. 4 (1974).MathSciNetGoogle Scholar
  4. 4.
    Seshadri R., Group Theoretic Methods of Similarity Analysis Applied to Nonlinear Impact Problems, Ph.D. thesis, Univ. of Calgary, Alberta,Canada (1973).Google Scholar
  5. 5.
    Birkhoff G., Hydrodynamics, Princeton University Press, New Jersey (1960).Google Scholar
  6. 6.
    Nowacki W., Dynamics of Elastic Systems, Chapman and Hall Ltd., London (1963).Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1985

Authors and Affiliations

  • R. Seshadri
    • 1
  • T. Y. Na
    • 2
  1. 1.Syncrude Canada LimitedFort McMurrayCanada
  2. 2.Department of Mechanical EngineeringUniversity of Michigan—DearbornDearbornUSA

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