## Advances in Differential Equations

- Adv. Differential Equations
- Volume 14, Number 11/12 (2009), 1085-1106.

### Very slow convergence to zero for a supercritical semilinear parabolic equation

#### Abstract

We study the asymptotic behavior of nonnegative solutions to the Cauchy problem for a semilinear parabolic equation with a supercritical nonlinearity. It is known that there are initial data such that the corresponding solution decays to zero with an algebraic rate. Furthermore, any algebraic rate which is slower than the self-similar rate occurs as decay rate for some solution. In this paper we prove that the convergence to zero can take place with an "arbitrarily" slow rate, if the initial data are chosen properly.

#### Article information

**Source**

Adv. Differential Equations, Volume 14, Number 11/12 (2009), 1085-1106.

**Dates**

First available in Project Euclid: 18 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1355854785

**Mathematical Reviews number (MathSciNet)**

MR2560869

**Zentralblatt MATH identifier**

1190.35035

**Subjects**

Primary: 35K15: Initial value problems for second-order parabolic equations 35B40: Asymptotic behavior of solutions 35K57: Reaction-diffusion equations

#### Citation

Stinner, Christian. Very slow convergence to zero for a supercritical semilinear parabolic equation. Adv. Differential Equations 14 (2009), no. 11/12, 1085--1106. https://projecteuclid.org/euclid.ade/1355854785