Life span of positive solutions for a semilinear heat equation with non-decaying initial data

Abstract

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.