Electronic Journal of Differential Equations,
Conference 08 (2002), pp. 85-101

Title: Description of regional blow-up in a porous-medium equation

Authors: Carmen Cort'azar (Univ. de Chile, Santiago, Chile)
 Manuel del Pino (Univ. de Chile, Santiago, Chile)
 Manuel Elgueta (Univ. de Chile, Santiago, Chile)
 
Abstract: 
We describe the (finite-time) blow-up phenomenon for a non-negative 
 solution of a porous medium equation of the form 
 $$
 u_t = \Delta u^m + u^m  
 $$
 in the entire space. Here $m>1$ and the initial condition is 
 assumed compactly supported. Blow-up takes place exactly inside a 
 finite number of balls with same radii and exhibiting the same 
 self-similar profile. 

Published October 21, 2002.
Math Subject Classifications: 35B40, 35B45, 35J40.
Key Words: Multiple-bump; pattern formation; mathematical biology;
singular perturbation.