Blow-up for a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions

Youpeng Chen, and Baozhu Zheng. "Blow-up for a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions." Annales Polonici Mathematici 114.2 (2015): 179-196. <http://eudml.org/doc/280883>.

@article{YoupengChen2015,
abstract = {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.},
author = {Youpeng Chen, Baozhu Zheng},
journal = {Annales Polonici Mathematici},
keywords = {localized singular parabolic equation; nonlocal nonlinear boundary condition; global existence; global blow-up; uniform blow-up profile},
language = {eng},
number = {2},
pages = {179-196},
title = {Blow-up for a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions},
url = {http://eudml.org/doc/280883},
volume = {114},
year = {2015},
}

TY - JOUR
AU - Youpeng Chen
AU - Baozhu Zheng
TI - Blow-up for a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions
JO - Annales Polonici Mathematici
PY - 2015
VL - 114
IS - 2
SP - 179
EP - 196
AB - 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.
LA - eng
KW - localized singular parabolic equation; nonlocal nonlinear boundary condition; global existence; global blow-up; uniform blow-up profile
UR - http://eudml.org/doc/280883
ER -