We consider an estimate of the life span of solutions on a semilinear heat equation. In one dimension, we show that the life span may be estimated from above in terms of the average of two limits as $x\to\pm\infty$ of the initial data. In general dimensions, under some monotonicity conditions for initial data, an explicit representation of the uniform norm of the life span of solutions is obtained.
"Life span of positive solutions for a semilinear heat equation with non-decaying initial data." Differential Integral Equations 23 (11/12) 1151 - 1157, November/December 2010. https://doi.org/10.57262/die/1356019078