2001-Luminy conference on Quasilinear Elliptic and Parabolic Equations and Systems
Electron. J. Diff. Eqns., Conf. 08, 2002, pp. 85-101.

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

Carmen Cortazar, Manuel del Pino, & Manuel Elgueta

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 $m$ greater than 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.

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Carmen Cortazar
Departamento de Matematicas
Pontificia Universidad Catolica de Chile
Casilla 306, Correo 22, Santiago, Chile
e-mail: ccortaza@mat.puc.cl

Manuel del Pino
Departamento de Ingenieria Matematica and CMM
Universidad de Chile
Casilla 170 Correo 3, Santiago, Chile
e-mail: delpino@dim.uchile.cl

Manuel Elgueta
Departamento de Matematicas
Pontificia Universidad Catolica de Chile
Casilla 306, Correo 22, Santiago, Chile
e-mail: melgueta@mat.puc.cl

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