(untitled) (Journal of Partial Differential Equations, 2020)
" In this paper, we consider the existence and nonexistence of global solutions to the semilinear heat equation u_t - 0394u = u^p with Neumann boundary value frac2202u220203bd = 0 on some unbounded domains, where p > 1, 03bd is the outward normal vector on boundary 220203a9. We prove that there exists a critical exponent p_c = p_c(03a9) > 1 such that if p 2208 (1, p_c], for nonnegative and nontrivial initial data, all positive solutions blow up in finite time; if p > p_c, for suitably small nonnegative initial data, there exists a global positive solution."