Article
Combining fast, linear and slow diffusion
Author/s | López Gómez. Julián
Suárez Fernández, Antonio ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2004 |
Deposit Date | 2016-05-17 |
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Abstract | Although 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] ... Although 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. |
Funding agencies | Ministerio de Ciencia y Tecnología (MCYT). España |
Project ID. | BFM2000-0797
![]() BFM2003-06466 ![]() REN2003-00707 ![]() |
Citation | López Gómez, J. y Suárez Fernández, A. (2004). Combining fast, linear and slow diffusion. Topological Methods in Nonlinear Analysis, 23, 275-300. |
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