@Article{JPDE-17-351,
author = {Yonggeng Gu  and Wenjun Sun },
title = {Existence and Nonexistence of Global Solutions for Semilinear Heat Equation on Unbounded Domain},
journal = {Journal of Partial Differential Equations},
year = {2004},
volume = {17},
number = {4},
pages = {351--368},
abstract = {<p>In this paper, we consider the existence and nonexistence of global solutions to the semilinear heat equation u_t - Δu = u^p with Neumann boundary value \frac{∂u}{∂ν} = 0 on some unbounded domains, where p &gt; 1, ν is the outward normal vector on boundary ∂Ω. We prove that there exists a critical exponent p_c = p_c(Ω) &gt; 1 such that if p ∈ (1, p_c], for nonnegative and nontrivial initial data, all positive solutions blow up in finite time; if p &gt; p_c, for suitably small nonnegative initial data, there exists a global positive solution.</p>},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5398.html}
}