EXISTENCE AND NON-UNIQUENESS OF SIMILARITY SOLUTIONS OF A BOUNDARY-LAYER PROBLEM

摘要

This work considers a Blasius boundary-value problem with inhomogeneous lower-boundary conditionsf(0)=0 andf'(0)=–λwithλstrictly positive. The Crocco-variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary-value problem do not exist for values ofλlarger than a positive critical valueλ*. The existence of solutions is proved for 0<λ≤λ*by considering an equivalent initial-value problem. However, for 0<λ<λ*, solutions of the boundary-value problem are found to be non-unique. Physically, this non-uniqueness is related to multiple values of the sk