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

Volume 114 / 2015

Youpeng Chen, Baozhu Zheng 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.

Authors

  • Youpeng ChenSchool of Mathematics
    Yancheng Normal University
    Yancheng 224002, P.R. China
    e-mail
  • Baozhu ZhengDepartment of Mathematics
    Qinghai Normal University
    Xining 810008, P.R. China
    e-mail

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