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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-7,
author = {Zhiyong Wang and Jingxue Yin},
title = {Note on blow-up of solutions for a porous medium equation with convection and boundary flux},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {223-228},
zbl = {1262.35059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-7}
}
Zhiyong Wang; Jingxue Yin. Note on blow-up of solutions for a porous medium equation with convection and boundary flux. Colloquium Mathematicae, Tome 126 (2012) pp. 223-228. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-7/