Similarity Analysis of Boundary Value Problems with Finite Boundaries

R. Seshadri and T. Y. Na
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R. Seshadri: Syncrude Canada Limited
T. Y. Na: University of Michigan—Dearborn, Department of Mechanical Engineering

Chapter Chapter 5 in Group Invariance in Engineering Boundary Value Problems, 1985, pp 91-102 from Springer

Abstract: 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: Similarity Solution; Auxiliary Condition; Finite Domain; Affine Group; Infinite Domain (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-1-4612-5102-6_5

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