Life span of solutions for a quasilinear parabolic equation with initial data having positive limit inferior at infinity

Abstract

We present a new upper bound of the life span of positive solutions of a quasilinear parabolic equation for the initial data having positive limit inferior at space infinity. The upper bound is expressed by the data in limit inferior, not in every direction, but around a specific direction. It is also shown that the minimal time blow-up occurs when the initial data attain its maximum at space infinity.