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

• 作者: Baozhu Zheng Youpeng Chen
• 来源期刊: 微分方程年刊：英文版
• 学科: 数学
• 关键词: 非局部边界条件 抛物型方程 BLOW-UP 本地化 加权 奇异 退化 有限时间
• 年，卷（期）: 2014,（4）
• 页码范围: 484-493
• 页数: 10页
• 分类号: O175.25

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 conditions. 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.