Existence of solutions of a generalized Blasius equation

Abstract

The theorem established includes, as a special case, the existence and uniqueness of solutions of the Falkner-Skan problem, where .f(y”) = X(1 Y’~), h > 0, and its special cases such as the Homan problem (A = t). The Blasius problem, h = 0, is omitted for convenience but, of course, it is well-known that it has a unique solution. So far as the special case of the Falkner-Skan problem, per se, is concerned the results of the paper are known. In this paper we establish a unique solution for a rather general boundary problem that includes problems frequently encountered in the study of boundary layer theory, the flow of fluids in general and, hopefully, elsewhere. The book [13] of H. Schlichting is a classical reference to boundary layer theory. The mathematics of the Falkner-Skan problem prior to about 1963 is very well brought together by Philip Hartman [7]. Major papers prior to 1963 include the original Falkner-Skan paper [6], papers of H. Weyl [14], W. A. Coppel [5] (which was prepared independently of the significant papers [I 1, 121 of R. Iglisch) and a paper of Philip Hartman [8] d evoted especially to the asymptotic behavior of solutions. Recent papers (of which [l, 2, 3, 4, 9, 101 are only a sample) have contributed to certain refinement questions such as reverse flow possibilities, further asymptotic properties, etc. In the present paper we are concerned with the existence and uniqueness of solutions of (1) with boundary conditions