Geodesic
Existence of scale invariant solutions to horizontal flow with a Fujita type diffusion coefficient
Electronic Journal of Differential Equations, Tome 2012 (2012).

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

Summary: 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},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a60/}
}
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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/