Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 78, pp. 1-15.
Title: On singular solutions of a magnetohydrodynamic nonlinear
boundary layer equation
Authors: Mohammed Benlahsen (Univ. de Picardie Jules Verne, Amiens, France)
Abdelilah Gmira (Univ. Abdelamelk Assaadi, Tetouan, Maroc)
Mohammed Guedda (Univ. de Picardie Jules Verne, Amiens, France)
Abstract:
This paper concerns the singular solutions of the equation
$$
f''' +\kappa ff''-\beta {f'}^2 = 0,
$$
where $\beta < 0$ 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.