ON THE ASYMPTOTIC SOLUTION OF LAMINAR CHANNEL FLOW WITH LARGE SUCTION

The equation considered is epsilon f(iv) = ff''' - f'f '', with bounda ry conditions f(0) = f ''(0) = 0, f(1) = 1, f'(1) = 0. When 0 < epsilo n much less than 1, the boundary value problem corresponds to the lami nar flow of a viscous fluid through a porous channel under large sucti on. It is known that there are three solutions in this case: two of th em are monotone increasing (types I and II), and the third is nonmonot one (type III). Let (1-Delta) be the turning point of f(eta) in (0, 1) . This paper presents a rigorous proof of the asymptotic behavior of t ype III solutions, which is f(eta) similar to kappa sin pi eta/1-Delta , where kappa similar to 1-Delta/pi Delta and Delta/epsilon e(Delta/ep silon) similar to 1/2e pi(9) epsilon(8), uniformly on [0, 1-Delta] as epsilon --> O+, and provides detailed information at the turning point .