Geodesic
Radial selfsimilar solutions of a nonlinear Ornstein-Uhlenbeck equation
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a239/}
}
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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__a239/