Blow-up versus extinction in a nonlocal p-Laplace equation with Neumann boundary conditions ☆
Blow-up versus extinction in a nonlocal p-Laplace equation with Neumann boundary conditions ☆
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DOI：
10.1016/j.jmaa.2013.10.040
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发表时间：
2014-04
影响因子：
1.3
通讯作者：
Chengyuan Qu;Xueli Bai;Sining Zheng
中科院分区：
文献类型：
--
作者：
Chengyuan Qu;Xueli Bai;Sining Zheng
研究了一类带非局部源的快扩散p-Laplace方程|u| q− Ω| u|有界区域中的q dx，服从齐次Neumann边值条件。得到了一个临界准则，即当q> 1且初始能量为非正时，变号解在有限时间内爆破，且当q ≥ 1时，变号解对任意初始能量都是整体解.特别地，得到了变号解在有限时间内消失的条件。
This paper studies a fast diffusive p-Laplace equation with the nonlocal source| u| q−⨍ Ω| u| q d x in a bounded domain, subject to homogeneous Neumann boundary value condition. A critical criterion is determined that the changing sign solutions blow up in finite time with q> 1 and non-positive initial energy associated, and must be global for any initial energy if q⩽ 1. In particular, the conditions are obtained under which the changing sign solutions vanish in finite time.