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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
Yūki Naito
Affiliation:
Department of Applied Mathematics, Faculty of Engineering, Kobe University, Nada, Kobe 657-8501, Japan ([email protected])
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Abstract

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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 4 , August 2006 , pp. 807 - 835
Copyright
Copyright © Royal Society of Edinburgh 2006

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