Hostname: page-component-7b9c58cd5d-dlb68 Total loading time: 0 Render date: 2025-03-15T16:48:57.320Z Has data issue: false hasContentIssue false

An ODE approach to the multiplicity of self-similar solutions for semi-linear heat equations

Published online by Cambridge University Press:  12 July 2007

Yūki Naito
Affiliation:
Department of Applied Mathematics, Faculty of Engineering, Kobe University, Nada, Kobe 657-8501, Japan (naito@cs.kobe-u.ac.jp)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Cauchy problem for semi-linear heat equations with singular initial data is studied, where N > 2, p > (N + 2)/N, and l > 0 is a parameter. We establish the existence and multiplicity of positive self-similar solutions for the problem by applying the ordinary differential equation shooting method to the corresponding spatial profile problem.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2006