Geodesic
Radial selfsimilar solutions of a nonlinear Ornstein-Uhlenbeck equation
Electronic journal of differential equations, Tome 2007 (2007)
This paper concerns the existence, uniqueness and asymptotic properties (as

$ v_t=\Delta_p v+x\cdot\nabla (|v|^{q-1}v) $

in

$ v(x,t)=t^{-\gamma} U(cxt^{-\sigma}), $

where

$ (|u'|^{p-2}u')'+\frac{N-1}r |u'|^{p-2}u'+\frac{q+1-p}{p} r u'+(q-1) r(|u|^{q-1}u)'+u=0 $

in $\mathbb{R}_+$. We carry out a careful analysis of this equation and deduce the corresponding consequences for the Ornstein-Uhlenbeck equation.
Classification : 34L30, 35K55, 35K65
Keywords: p-Laplacian, Ornstein-Uhlenbeck diffusion equations, self-similar solutions, shooting technique 
@article{EJDE_2007__2007__a39,
     author = {Bouzelmate,  Arij and Gmira,  Abdelilah and Reyes,  Guillermo},
     title = {Radial selfsimilar solutions of a nonlinear {Ornstein-Uhlenbeck} equation},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1146.34004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a39/}
}
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%A Reyes,  Guillermo
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%G en
%F EJDE_2007__2007__a39
Bouzelmate,  Arij; Gmira,  Abdelilah; Reyes,  Guillermo. Radial selfsimilar solutions of a nonlinear Ornstein-Uhlenbeck equation. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a39/