This paper deals with the blow-up properties of positive solutions to a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions. Under certain conditions, criteria of global existence and finite time blow-up are established. Furthermore, when q=1, the global blow-up behavior and the uniform blow-up profile of the blow-up solution are described; we find that the blow-up set is the whole domain [0,a], including the boundary, in contrast to the case of parabolic equations with local sources or with homogeneous Dirichlet boundary conditions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap114-2-7,
author = {Youpeng Chen and Baozhu Zheng},
title = {Blow-up for a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions},
journal = {Annales Polonici Mathematici},
volume = {113},
year = {2015},
pages = {179-196},
zbl = {1322.35088},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap114-2-7}
}
Youpeng Chen; Baozhu Zheng. Blow-up for a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions. Annales Polonici Mathematici, Tome 113 (2015) pp. 179-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap114-2-7/