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October  2005, 12(5): 929-948. doi: 10.3934/dcds.2005.12.929

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, France, France

Received  December 2003 Revised  October 2004 Published  February 2005

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.
Keywords: boundary value problem, Third order differential equation, plane dynamical system., blowing-up coordinates.
Mathematics Subject Classification: 34B15, 34C11, 76D1.
Citation: Bernard Brighi, Tewfik Sari. Blowing-up coordinates for a similarity boundary layer equation. Discrete & Continuous Dynamical Systems, 2005, 12 (5) : 929-948. doi: 10.3934/dcds.2005.12.929
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