Similarity Analysis of Boundary Value Problems with Finite Boundaries

  • R. Seshadri
  • T. Y. Na

Abstract

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.

Keywords

Nite Clarification 

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References

  1. 1.
    Hansen A.G., Similarity Analysis of Boundary Value Problems in Engineering, Princeton Hall (1960).Google Scholar
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    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
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    Seshadri R., Group Theoretic Methods of Similarity Analysis Applied to Nonlinear Impact Problems, Ph.D. thesis, Univ. of Calgary, Alberta,Canada (1973).Google Scholar
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    Birkhoff G., Hydrodynamics, Princeton University Press, New Jersey (1960).Google Scholar
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    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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