Geodesic
Blow-up for a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions
Youpeng Chen1 ; Baozhu Zheng2
1School of Mathematics Yancheng Normal University Yancheng 224002, P.R. China
2Department of Mathematics Qinghai Normal University Xining 810008, P.R. China
Annales Polonici Mathematici, Tome 114 (2015) no. 2, pp. 179-196
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap114-2-7
Keywords: paper deals blow up properties positive solutions localized singular parabolic equation weighted nonlocal nonlinear boundary conditions under certain conditions criteria global existence finite time blow up established furthermore global blow up behavior uniform blow up profile blow up solution described blow up set whole domain including boundary contrast parabolic equations local sources homogeneous dirichlet boundary conditions

Youpeng Chen  1   ; Baozhu Zheng  2

1 School of Mathematics Yancheng Normal University Yancheng 224002, P.R. China
2 Department of Mathematics Qinghai Normal University Xining 810008, P.R. China 
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Youpeng Chen; Baozhu Zheng. Blow-up for a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions. Annales Polonici Mathematici, Tome 114 (2015) no. 2, pp. 179-196. doi: 10.4064/ap114-2-7

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