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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Fujishima, Yohei¹  Ishige, Kazuhiro¹ 

[1] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

关键词: Blow-up problem;    Semi linear heat equation;    Large diffusion;    Blow-up set;    Hot spots;   

DOI  :  10.1016/j.jde.2011.08.040

来源: Elsevier

【 摘 要 】

We are concerned with the Cauchy problem for a semilinear heat equation, {partial derivative(t)u = D Delta u + vertical bar u vertical bar(p-1)(u), x is an element of R(N), u (x, 0) = lambda + phi (X), x is an element of R(N), (P) where D > 0, p > 1, N >= 3, lambda > 0, and phi is an element of L(infinity) (R(N)) boolean AND L(1) (R(N), (1 + vertical bar x vertical bar)(2) dx). In the paper of Fujishima and lshige (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 -> infinity for the case integral(R)N phi (x) dx > 0. In this paper, as a continuation of Fujishima and Ishige (2011) [8], we consider the case integral(R)N phi (x) dx <= 0, and study the behavior of the blow-up time and the blow-up set of the solution of (P) as D -> infinity. The behavior in the case integral(R)N phi (x) dx <= 0 is completely different from the one in the case integral(R)N phi (x) dx > 0. (C) 2011 Elsevier Inc. All rights reserved.

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