Geodesic
On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation
Electronic journal of differential equations, Tome 2007 (2007)
This paper concerns the singular solutions of the equation

$ f''' +\kappa ff''-\beta {f'}^2 = 0, $

where $\beta$ 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.
Classification : 34C11, 76D10
Keywords: boundary-layer equation, MHD flow, blowing-up solutions, asymptotic behavior 
@article{EJDE_2007__2007__a48,
     author = {Benlahsen,  Mohammed and Gmira,  Abdelilah and Guedda,  Mohammed},
     title = {On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1140.34357},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a48/}
}
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Benlahsen,  Mohammed; Gmira,  Abdelilah; Guedda,  Mohammed. On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a48/