Geodesic
Existence of scale invariant solutions to horizontal flow with a Fujita type diffusion coefficient
Electronic journal of differential equations, Tome 2012 (2012)
In this article, we study a boundary-initial value problem on the half-line for the diffusion equation with a Fujita type diffusion coefficient that carries a parameter $\alpha $. The equation models the flow of water in soil within an approximation where gravitational effects are not taken into account and, when $\alpha = 1$, an explicit self-similar solution $\psi(x/\sqrt t)$ can be found. We prove that if $\alpha > 1$ then the above problem, with uniform boundary conditions, posses self-similar solutions. This is the first step towards a multiscale (renormalization group) asymptotic analysis of solutions to more general equations than the ones studied here.
Classification : 34E10, 34E13, 35C06, 35Q86
Keywords: water infiltration, nonlinear diffusion, self-similar solutions, Fujita diffusion coefficient 
@article{EJDE_2012__2012__a60,
     author = {Braga,  Gastao A. and Carriao,  Paulo C. and Ruas,  Antonio A.G.},
     title = {Existence of scale invariant solutions to horizontal flow with a {Fujita} type diffusion coefficient},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1259.35051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a60/}
}
TY  - JOUR
AU  - Braga,  Gastao A.
AU  - Carriao,  Paulo C.
AU  - Ruas,  Antonio A.G.
TI  - Existence of scale invariant solutions to horizontal flow with a Fujita type diffusion coefficient
JO  - Electronic journal of differential equations
PY  - 2012
VL  - 2012
UR  - http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a60/
LA  - en
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%A Carriao,  Paulo C.
%A Ruas,  Antonio A.G.
%T Existence of scale invariant solutions to horizontal flow with a Fujita type diffusion coefficient
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a60/
%G en
%F EJDE_2012__2012__a60
Braga,  Gastao A.; Carriao,  Paulo C.; Ruas,  Antonio A.G. Existence of scale invariant solutions to horizontal flow with a Fujita type diffusion coefficient. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a60/