Self-similar solutions of the p-Laplace heat equation: the case when p > 2
Published online by Cambridge University Press: 13 March 2009
Abstract
We study the self-similar solutions of the equation
in ℝN, when p > 2. We make a complete study of the existence and possible uniqueness of solutions of the form
of any sign, regular or singular at x = 0. Among them we find solutions with an expanding compact support or a shrinking hole (for t > 0), or a spreading compact support or a focusing hole (for t < 0). When t < 0, we show the existence of positive solutions oscillating around the particular solution .
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 1 , February 2009 , pp. 1 - 43
- Copyright
- Copyright © Royal Society of Edinburgh 2009
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