Blow-up for a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions
Volume 114 / 2015
Annales Polonici Mathematici 114 (2015), 179-196
MSC: Primary 35K57, 35K61; Secondary 35B40, 35K65.
DOI: 10.4064/ap114-2-7
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.
