Description

• Title:
  Combining fast, linear and slow diffusion
• Creator:
  López-Gómez, Julian;
  Suárez, Antonio
• Description:
  Although the pioneering studies of G. I. Barenblatt [< i> On some unsteady motions of a liquid or a gas in a porous medium< /i> , Prikl. Mat. Mekh. < b> 16< /b> (1952), 67–68] and A. G. Aronson and L. A. Peletier [< i> Large time behaviour of solutions of some porous medium equation in bounded domains< /i> , J. Differential Equations < b> 39< /b> (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 {\it fast diffusion behavior}, whereas the remaining states are rather reminiscent of the purely {\it 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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2004.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 23, No 2 (June 2004); 275 - 300;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2004.012/9226
• Subject:
  Heterogeneous nonlinear diffusion;
  fast;
  slow and linear diffusion;
  35B32;
  35J25;
  35J60;
  35K57
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2004.012
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other