## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Asymptotic Analysis and Singularities — Elliptic and parabolic PDEs and related problems, H. Kozono, T. Ogawa, K. Tanaka, Y. Tsutsumi and E. Yanagida, eds. (Tokyo: Mathematical Society of Japan, 2007), 675 - 688

### A variational approach to self-similar solutions for semilinear heat equations

#### Abstract

We study the existence of self-similar solutions for semilinear heat equations by making use of the methods for semilinear elliptic equations. In particular, via the variational approach, we show the existence of the second solution, which implies the non-uniqueness of solutions to the Cauchy problem for semilinear heat equations with singular initial data.

#### Article information

**Dates**

Received: 27 October 2005

Revised: 21 December 2005

First available in Project Euclid:
16 December 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1545000902

**Digital Object Identifier**

doi:10.2969/aspm/04720675

**Mathematical Reviews number (MathSciNet)**

MR2387264

**Zentralblatt MATH identifier**

1141.35394

#### Citation

Naito, Yūki. A variational approach to self-similar solutions for semilinear heat equations. Asymptotic Analysis and Singularities — Elliptic and parabolic PDEs and related problems, 675--688, Mathematical Society of Japan, Tokyo, Japan, 2007. doi:10.2969/aspm/04720675. https://projecteuclid.org/euclid.aspm/1545000902