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

Yūki Naito

doi:10.1017/S0308210500004741

Abstract

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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.

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

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