A REMARK ON THE ENERGY BLOW-UP BEHAVIOR FOR NONLINEAR HEAT EQUATIONS
A REMARK ON THE ENERGY BLOW-UP BEHAVIOR FOR NONLINEAR HEAT EQUATIONS
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非线性热方程能量爆炸行为的评述
DOI：
10.1215/s0012-7094-00-10336-5
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发表时间：
2000
影响因子：
2.5
通讯作者：
H. Zaag
中科院分区：
文献类型：
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作者：
H. Zaag
lim t→t‖u(t)‖h10() =+∞。若点A∈存在（an, tn）→（A，T），使得|u(an, tn)|→+∞，则称点A∈为u的爆破点。u(t)的所有爆破点的集合称为爆破集，记为s。从Giga和Kohn[8，定理5.3]可知，∂中不存在爆破点。因此，由(3)可知，S的有界性不为空。许多论文关注的是(1)的柯西问题（参见，例如，[21]）或在初始数据上找到充分爆破条件的问题(参见
lim t→T ‖u(t)‖H 1 0 ( ) =+∞. A point a ∈ is called a blow-up point of u if there exists (an, tn) → (a,T ) such that |u(an, tn)| → +∞. The set of all blow-up points of u(t) is called the blow-up set and denoted by S. From Giga and Kohn [8, Theorem 5.3], there are no blow-up points in ∂ . Therefore, we see from (3) and the boundedness of that S is not empty. Many papers are concerned with the Cauchy problem for (1) (see, for instance, [21]) or the problem of finding sufficient blow-up conditions on the initial data (see