Blowing-up coordinates for a similarity boundary layer equation

Bernard Brighi; Tewfik Sari

doi:10.3934/dcds.2005.12.929

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2005, Volume 12, Issue 5: 929-948. Doi: 10.3934/dcds.2005.12.929

This issue Previous Article $L^\infty$ jenergies on discontinuous functions Next Article Non-existence of global solutions for nonlinear strongly damped hyperbolic systems

Blowing-up coordinates for a similarity boundary layer equation

Bernard Brighi^1, and
Tewfik Sari^1,

1.
Université de Haute Alsace, Laboratoire de mathématiques, F.S.T., 4 rue des frères Lumière, 68093 MULHOUSE

Received: November 30, 2003

Revised: September 30, 2004

Published: September 2005

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Abstract

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.

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Mathematics Subject Classification: 34B15, 34C11, 76D10.

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