Blow-up and extinction for a thin-film equation with initial-boundary value conditions
Blow-up and extinction for a thin-film equation with initial-boundary value conditions
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DOI：
10.1016/j.jmaa.2015.11.075
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发表时间：
2016-04
影响因子：
1.3
通讯作者：
Chengyuan Qu;Wenshu Zhou
中科院分区：
文献类型：
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作者：
Chengyuan Qu;Wenshu Zhou
本文考虑一类具有非局部源的薄膜方程的初边值问题|u| q− Ω| u|有界域中的q d x。由于比较原理无效，我们利用势井方法给出了变号弱解整体存在和不存在的阈值结果。在此基础上，我们得到了整体解在有限时间内灭绝的条件，并研究了非灭绝解的渐近性态。
In this paper, we consider an initial-boundary value problem for a thin-film equation, with the nonlocal source| u| q−⨍ Ω| u| q d x in a bounded domain. Due to the comparison principle being invalid, we use the potential well method to give a threshold result of global existence and non-existence for the sign-changing weak solutions. Further, we obtain the conditions under which the global solutions extinct in finite time and study the asymptotic behavior of the non-extinct solutions.