Blow-up phenomena for a class of fourth-order parabolic problems
Blow-up phenomena for a class of fourth-order parabolic problems
复制标题
一类四阶抛物线问题的爆炸现象
DOI：
10.1090/s0002-9939-2015-12446-x
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
G. Philippin
中科院分区：
文献类型：
--
作者：
G. Philippin
摘要。本文讨论了一类半线性四阶抛物型问题解的一些定性性质。证明了在数据的一定条件下，u（x, t）不可能一直存在，并导出了t的上界，其中（0,t）是u（x, t）存在的区间。此外，我们（在数据的一定条件下）构造了爆炸发生时t的下界。最后的结果是基于本文最后建立的Sobolev型不等式。
Abstract. This paper deals with some qualitative properties of solutions to a class of semilinear fourth-order parabolic problems. It is shown that under certain conditions on the data, u(x, t) cannot exist for all time and an upper bound for t is derived where (0, t ) is the interval of existence of u(x, t). Moreover we construct (under certain conditions on the data) a lower bound for t when blow-up occurs. This last result is based on some Sobolev type inequality established at the end of the paper.