Similarity Analysis of Boundary Value Problems with Finite Boundaries
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.
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- 1.Hansen A.G., Similarity Analysis of Boundary Value Problems in Engineering, Princeton Hall (1960).Google Scholar
- 2.Carslaw H.S. and Jaeger J.C., Conduction of Heat in Solids, 2nd edition,Oxford Univ. Press,London (1959).Google Scholar
- 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.Birkhoff G., Hydrodynamics, Princeton University Press, New Jersey (1960).Google Scholar
- 6.Nowacki W., Dynamics of Elastic Systems, Chapman and Hall Ltd., London (1963).Google Scholar