Blow-up for a semilinear parabolic equation with large diffusion on RN. II

Yohei Fujishima, Kazuhiro Ishige

研究成果: Article査読

10 被引用数 (Scopus)

抄録

We are concerned with the Cauchy problem for a semilinear heat equation,(P){∂tu=Dδu+|u|p-1u,x∈RN,t>0,u(x,0)=λ+φ(x),x∈RN, 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 ∫RNφ(x)dx>0. In this paper, as a continuation of Fujishima and Ishige (2011) [8], we consider the case∫RNφ(x)dx≤0, 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 ∫RNφ(x)dx≤0 is completely different from the one in the case ∫RNφ(x)dx>0.

本文言語English
ページ(範囲)1835-1861
ページ数27
ジャーナルJournal of Differential Equations
252
2
DOI
出版ステータスPublished - 2012 1 15

ASJC Scopus subject areas

  • 分析
  • 応用数学

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