Electron. J. Diff. Eqns., Vol. 2007(2007), No. 78, pp. 1-15.

On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation

Mohammed Benlahsen, Abdelilah Gmira, Mohammed Guedda

Abstract:
This paper concerns the singular solutions of the equation
$$ f''' +\kappa ff''-\beta {f'}^2 = 0, $$
where $\beta$ less than 0 and $\kappa = 0$ or 1. This equation arises when modelling heat transfer past a vertical flat plate embedded in a saturated porous medium with an applied magnetic field. After suitable normalization, $f'$ represents the velocity parallel to the surface or the non-dimensional fluid temperature. Our interest is in solutions which develop a singularity at some point (the blow-up point). In particular, we shall examine in detail the behavior of $f$ near the blow-up point.

Submitted September 22, 2006. Published May 23, 2007.
Math Subject Classifications: 34C11, 76D10.
Key Words: Boundary-layer equation; MHD flow; blowing-up solutions; asymptotic behavior.

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Mohammed Benlahsen
LPMC, Université de Picardie Jules Verne
Faculté des Sciences, 33, rue Saint-Leu 80039 Amiens, France
email: benlahsen@u-picardie.fr
Abdelilah Gmira
Département de Mathématiques et Informatique
Faculté des Sciences, BP 2121, Tétouan, Maroc
email: gmira@fst.ac.ma or gmira.i@menara.ma
Mohammed Guedda
Lamfa, CNRS UMR 6140, Université de Picardie Jules Verne
Faculté de Mathématiques et d'Informatique
33, rue Saint-Leu 80039, Amiens, France
email: guedda@u-picardie.fr

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