A two-point boundary value problem arising in boundary layer theory

Abstract

A two-point boundary value problem of second order is restudied, which describes both a similarity boundary-layer flow induced by a moving permeable plane surface and a self-similar free convection boundary-layer flow over a vertical permeable flat plate embedded in a fluid-saturated porous medium. It is proved that there exists a λmin∈[1,2/3] such that this problem has a unique normal solution ϕ(η;λ) for all λ⩾λmin and the solution ϕ(η;λ) is strictly decreasing with respect to both η⩾0 and λ⩾λmin; moreover, ϕ′(0;λmin)=0 and ϕ′(0;λ), as a function of λ, is strictly decreasing for λ⩾λmin.