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.