Advanced Studies in Pure Mathematics

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

Yūki Naito

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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

Source
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

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


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