TY - JOUR
T1 - Existence and Nonexistence of Global Solutions for Semilinear Heat Equation on Unbounded Domain
JO - Journal of Partial Differential Equations
VL - 4
SP - 351
EP - 368
PY - 2004
DA - 2004/11
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5398.html
KW - Semilinear heat equation
KW - global existence
KW - critical exponent of Fu-jita' s type
AB - <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>