Differential and Integral Equations

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.

Article information

Source
Differential Integral Equations, Volume 23, Number 11/12 (2010), 1151-1157.

Dates
First available in Project Euclid: 20 December 2012