【摘 要】
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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
【机 构】
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Department of Mathematics of Hu’nan Normal University, Changsha, 410081;Academy of Mathematics and S
论文部分内容阅读
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.
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