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.