Note on blow-up of solutions for a porous medium equation with convection and boundary flux
Volume 128 / 2012
Colloquium Mathematicum 128 (2012), 223-228
MSC: Primary 35K55; Secondary 35B33.
DOI: 10.4064/cm128-2-7
Abstract
De Pablo et al. [Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), 513–530] considered a nonlinear boundary value problem for a porous medium equation with a convection term, and they classified exponents of nonlinearities which lead either to the global-in-time existence of solutions or to a blow-up of solutions. In their analysis they left open the case of a certain critical range of exponents. The purpose of this note is to fill this gap.
