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Similarity solutions of differential equations for boundary layer approximations in porous media. (English) Zbl 1084.34034

Summary: This paper is concerned with the ordinary differential equation \[ f''' + mff'' - \alpha {f'}^2 = 0 \] on \((0,+\infty)\), subject to the boundary conditions \[ f(0) = a, \quad f'(0) = b, \quad f'(\infty) = \lim_{t\to\infty} f'(t) = 0, \] in wich \(a\) and \(b\) are reals, \(m > 0\) and \(\alpha < 0\). Such problem, with \(m = \frac{\alpha+1}2\), \(a = 0\), and \(b = 1\), arises in the study of the free convection, along a vertical flat plate embedded in a porous medium.
The analysis deals with existence, nonuniqueness and large-\(t\) behaviour of solutions of the above problem under favourable conditions on \(m,\alpha,a\) and \(b\).

MSC:

34B40 Boundary value problems on infinite intervals for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B60 Applications of boundary value problems involving ordinary differential equations
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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