LIFE SPAN OF POSITIVE SOLUTIONS FOR A SEMILINEAR HEAT EQUATION WITH NON-DECAYING INITIAL DATA

摘要

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 → fcc 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.