Optimal estimate on life span for semilinear heat equations with non-rarefied sources at infinity

This paper is devoted to studying in R(n )x (0, T ) (n > 1) the Cauchy problem for a semilinear heat equation with source term f (x) non-rarefied at infinity, subjected to zero initial data. To such a problem, the novelty of this work lies in: (a) similar to no source case, non-rarefaction of f at infinity brings about its classical solution blowing up in a finite time T* > 0; (b) we derive the optimal upper and lower bound on the life span T*. This may throw some light on studies of life span. (c) 2024 Elsevier Inc. All rights reserved.