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A Note on the Existence of a Solution of the Falkner-Skan Equation

Published online by Cambridge University Press:  20 November 2018

K. Kuen Tam
K. Kuen Tam*
Affiliation:
McGill University, Montreal, Quebec
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We are concerned with the existence proof of solution of the Falkner-Skan equation

1

subject to boundary conditions

2

The first existence and uniqueness proof based on a fixed point theorem was given by Weyl [4] in 1942, with the added assumption that f' > 0. In 1960, Coppel [1] proved the existence (and uniqueness with the assumption 0 < f' < 1) by considering trajectories in the three-dimensional phase space.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 125 - 127
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Coppel, W. A., On a differential equation of boundary layer theory, Proc. Cambridge Phil. Soc. Series A 253 (1960), 101-136.Google Scholar
2. Ho, D. and Wilson, H. K., On the existence of a similarity solution for a compressible boundary layer, Arch. Rational Mech. Anal. 27 (1967), 165-174.Google Scholar
3. McLeod, J. B. and Serrin, J., The existence of similar solutions for laminar boundary layer problems, Arch. Rational Mech. Anal. 31 (1968), 288-303.Google Scholar
4. Weyl, H., On the differential equations of the simplest boundary layer problems, Ann. Math. 43 (1942), 381-407.Google Scholar