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Blowing-up coordinates for a similarity boundary layer equation

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  • We introduce blowing-up coordinates to study the autonomous third order nonlinear differential equation : $f'''+\frac{m+1}{2}ff''-m f'^2=0$ on $(0,\infty)$, subject to the boundary conditions $f(0)=a\in\mathbb R$, $f'(0)=1$ and $f'(t)\to 0$ as $t\to\infty$. This problem arises when looking for similarity solutions to problems of boundary-layer theory in some contexts of fluids mechanics, as free convection in porous medium or flow adjacent to a stretching wall. We study the corresponding plane dynamical systems and apply the results obtained to the original boundary value problem, in order to solve questions for which direct approach fails.
    Mathematics Subject Classification: 34B15, 34C11, 76D10.


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