### Threshold and strong threshold solutions of a semilinear parabolic equation

Pavol Quittner

#### Abstract

If $p>1+2/n$, then the equation $u_t-\Delta u = u^p, \quad x\in{\mathbb R}^n,\ t>0,$ possesses both positive global solutions and positive solutions which blow up in finite time. We study the large time behavior of radial positive solutions lying on the borderline between global existence and blow-up.

#### Article information

Source
Adv. Differential Equations Volume 22, Number 7/8 (2017), 433-456.

Dates
Accepted: October 2016
First available in Project Euclid: 4 May 2017