Blow-up for a semilinear parabolic equation with large diffusion on RN. II
Blow-up for a semilinear parabolic equation with large diffusion on RN. II
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DOI：
10.1016/j.jde.2011.08.040
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发表时间：
2011-03
影响因子：
2.4
通讯作者：
Y. Fujishima;Kazuhiro Ishige
中科院分区：
文献类型：
--
作者：
Y. Fujishima;Kazuhiro Ishige
本文研究半线性热方程的Cauchy问题，其中D>0，p>1，N <$3，λ>0，φ∈L∞（RN）<$L1（RN，（1+ 1））|X|）2dx）。在Fujishima和Ishige（2011）[8]的论文中，本文的作者研究了当D→∞时（P）解的爆破时间和爆破集的行为[公式：见正文]。作为Fujishima和Ishige（2011）[8]的继续，本文考虑了该情形，研究了（P）解在D→∞时的爆破时间和爆破集的行为.案例[Formula：see text]中的行为与案例[Formula：see text]中的行为完全不同。
We are concerned with the Cauchy problem for a semilinear heat equation, where D>0, p>1, N⩾3, λ>0, and φ∈L∞(RN)∩L1(RN,(1+|x|)2dx). In the paper of Fujishima and Ishige (2011) [8] the authors of this paper studied the behavior of the blow-up time and the blow-up set of the solution of (P) as D→∞ for the case [Formula: see text] . In this paper, as a continuation of Fujishima and Ishige (2011) [8], we consider the case and study the behavior of the blow-up time and the blow-up set of the solution of (P) as D→∞. The behavior in the case [Formula: see text] is completely different from the one in the case [Formula: see text] .