EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR SEMILINEAR HEAT EQUATION ON UNBOUNDED DOMAIN

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Semilinear heat equation global existence critical exponent of Fujita's type.
• 年，卷（期）: 2004,（4）
• 页码范围: 351-368
• 页数: 18页
• 分类号: O175.26,O175.29.
• 语种: 英文

摘要

In this paper, we consider the existence and nonexistence of global solutions to the semilinear heat equation ut - △u ＝ up with Neumann boundary valueu(σ)u/(σ)(v)=0 on some unbounded domains, where p ＞ 1,(v) is the outward normal vector on boundary (σ)Ω. We prove that there exists a critical exponent Pc ＝ Pc(Ω) ＞ 1 such that if p ∈(1, Pc], for nonnegative and nontrivial initial data, all positive solutions blow up in finite time; if p ＞ Pc, for suitably small nonnegative initial data, there exists a global positive solution.