### Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent

#### Abstract

We consider the Cauchy problem for a semilinear parabolic equation with a nonlinearity which is critical in the Joseph-Lundgren sense. We find the grow-up rate of solutions that approach a singular steady state from below as $t\to\infty$. The grow-up rate in the critical case contains a logarithmic term which does not appear in the Joseph-Lundgren supercritical case, making the calculations more delicate.

#### Article information

Source
Adv. Differential Equations Volume 12, Number 1 (2007), 1-26.

Dates
First available in Project Euclid: 18 December 2012

Mathematical Reviews number (MathSciNet)
MR2272819

Zentralblatt MATH identifier
1170.35456

#### Citation

Fila, Marek; King, John R.; Winkler, Michael; Yanagida, Eiji. Grow-up rate of solutions of a semilinear parabolic equation with a critical exponent. Adv. Differential Equations 12 (2007), no. 1, 1--26. https://projecteuclid.org/euclid.ade/1355867581.