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On a general similarity boundary layer equation
B. Brighi and J.-D. Hoernel
Received: July 17, 2006; Revised: November 26, 2007; Accepted: November 27, 2007
Abstract. In this paper we are concerned with the solutions of the differential equation f ''' + ff '' + g(f ') = 0 on [0,¥), satisfying the boundary conditions f(0) = a, f '(0) = b ³ 0, f '(¥) = l, and where g is some given continuous function. This general boundary value problem includes the Falkner-Skan case, and can be applied, for example, to free or mixed convection in porous medium, or flow adjacent to stretching walls in the context of boundary layer approximation. Under some assumptions on the function g, we prove existence and uniqueness of a concave or a convex solution. We also give some results about nonexistence and asymptotic behaviour of the solution.
Keywords: boundary layer; similarity solution; third order nonlinear differential equation; boundary value problem; Falkner-Skan; free convection; mixed convection.
AMS Subject classification: Primary: 34B15; 34C1; 76D10.
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