López Gómez. JuliánSuárez Fernández, Antonio2016-05-172016-05-172004López Gómez, J. y Suárez Fernández, A. (2004). Combining fast, linear and slow diffusion. Topological Methods in Nonlinear Analysis, 23, 275-300.1230-3429http://hdl.handle.net/11441/41295Although the pioneering studies of G. I. Barenblatt ([8] G. I. Barenblatt, On some unsteady motions of a liquid or a gas in a porous medium, Prikl. Mat. Mekh. 16 (1952), 67–68) and A. G. Aronson and L. A. Peletier ([7] A. G. Aronson and L. A. Peletier, Large time behaviour of solutions of some porous medium equation in bounded domains, J. Differential Equations 39 (1981), 378–412.) did result into a huge industry around the porous media equation, none further study analyzed the effect of combining fast, slow, and linear diffusion simultaneously, in a spatially heterogeneous porous medium. Actually, it might be this is the first work where such a problem has been addressed. Our main findings show how the heterogeneous model possesses two different regimes in the presence of a priori bounds. The minimal steady-state of the model exhibits a genuine fast diffusion behavior, whereas the remaining states are rather reminiscent of the purely slow diffusion model. The mathematical treatment of these heterogeneous problems should deserve a huge interest from the point of view of its applications in fluid dynamics and population evolution.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Heterogeneous nonlinear diffusionfastslow and linear diffusioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.12775/TMNA.2004.012