Arij Bouzelmate, Abdelilah Gmira, Guillermo Reyes
Abstract:
This paper concerns the existence, uniqueness and
asymptotic properties (as
) of radial self-similar
solutions to the nonlinear Ornstein-Uhlenbeck equation
in
. Here
,
,
and
denotes the
-Laplacian operator.
These solutions are of the form
where
and
are fixed powers given by the
invariance properties of differential equation, while
is a radial
function,
,
.
With the choice
,
the radial profile
satisfies the nonlinear ordinary differential
equation
in
.
We carry out a careful analysis of this equation and
deduce the corresponding consequences for the Ornstein-Uhlenbeck equation.
Submitted January 11, 2007. Published May 9, 2007.
Math Subject Classifications: 34L30, 35K55, 35K65.
Key Words: p-laplacian; Ornstein-Uhlenbeck diffusion equations;
self-similar solutions; shooting technique.
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Arij Bouzelmate Département de Mathématiques et Informatique Faculté des Sciences, BP 2121, Tétouan, Maroc email: bouzelmatearij@yahoo.fr |
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Abdelilah Gmira Département de Mathématiques et Informatique Faculté des Sciences, BP 2121, Tétouan, Maroc email: gmira@fst.ac.ma or gmira.i@menara.ma |
Guillermo Reyes Departamento de Matemáticas Universidad Carlos III de Madrid, Leganés, Madrid 28911, Spain email: greyes@math.uc3m.es |
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