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

An ODE approach to the multiplicity of self-similar solutions for semi-linear heat equations
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DOI：
10.1017/s0308210500004741
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发表时间：
2006-08
期刊：
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
影响因子：
--
通讯作者：
Y. Naito
Y. Naito
中科院分区：
其他
文献类型：
--
作者：
Y. Naito

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研究了具有奇异初值的半线性热方程的柯西问题，其中N&gt；2，p&gt；(N+2)/N，L&gt；0为参数。通过对相应的空间轮廓问题应用常微分方程打靶法，证明了该问题正自相似解的存在性和多解性。
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.