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GLOBAL BLOW-UP FOR A LOCALIZED DEGENERATE AND SINGULAR PARABOLIC EQUATION WITH WEIGHTED NONLOCAL BOUNDARY CONDITIONS 被引量：1

GLOBAL BLOW-UP FOR A LOCALIZED DEGENERATE AND SINGULAR PARABOLIC EQUATION WITH WEIGHTED NONLOCAL BOUNDARY CONDITIONS
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摘要 This paper deals with the blow-up properties of positive solutions to a localized degenerate and singular parabolic equation with weighted nonlocal boundary condi- tions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, the global blow-up behavior and the uniform blow-up profile of blow-up solutions are also described. We find that the blow-up set is the whole domain {0, a}, including the boundaries, and this differs from parabolic equations with local sources case or with homogeneous Dirichlet boundary conditions case. This paper deals with the blow-up properties of positive solutions to a localized degenerate and singular parabolic equation with weighted nonlocal boundary condi- tions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, the global blow-up behavior and the uniform blow-up profile of blow-up solutions are also described. We find that the blow-up set is the whole domain {0, a}, including the boundaries, and this differs from parabolic equations with local sources case or with homogeneous Dirichlet boundary conditions case.
作者 Baozhu Zheng Youpeng Chen
机构地区 Dept.of Math. School of Math.
出处 《Annals of Differential Equations》 2014年第4期484-493,共10页 微分方程年刊（英文版）
基金 supported by the research scheme of the natural science of the universities of Jiangsu province(08KJD110017 and 13KJB110028)
关键词 localized degenerate and singular parabolic equation weighted nonlo-cal boundary condition global existence finite time blow-up uniform blow-up profile localized degenerate and singular parabolic equation weighted nonlo-cal boundary condition global existence finite time blow-up uniform blow-up profile
分类号 O175.26 [理学—基础数学]
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Annals of Differential Equations
2014年 第4期

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