Summary
The Falkner-Skan equation f‴+ff″+λ(1-f′2)=0,f(0)=f′(0), is discussed for λ<0. Two types of problems, one with f′(∞)=1 and another with f′(∞)=-1, are considered. For λ=0- a close relation between these two types is found. For λ<-1 both types of problem allow multiple solutions which may be distinguished by an integer N denoting the number of zeros of f′-1. The numerical results indicate that the solution branches with f′(∞)=1 and those with f′(∞)=-1 tend towards a common limit curve as N increases indefinitely. Finally a periodic solution, existing for λ<-1, is presented.
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Oskam, B., Veldman, A.E.P. Branching of the Falkner-Skan solutions for λ<0. J Eng Math 16, 295–308 (1982). https://doi.org/10.1007/BF00037732
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DOI: https://doi.org/10.1007/BF00037732