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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Fujishima, Yohei¹  Ishige, Kazuhiro¹ 

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

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

DOI  :  10.1016/j.jde.2010.12.008

来源: Elsevier

【 摘 要 】

We consider 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, t > 0, u(x, 0) = lambda + phi(x), x is an element of R-N, 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 this paper we assume integral(N)(R) phi(x) dx > 0, and study the blow-up time and the location of the blow-up set of the solution for the case where D is sufficiently large. In particular, we prove that the location of the blow-up set depends on the large time behavior of the hot spots for the heat equation. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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