Self-similar solutions of the \(p\)-Laplace heat equation: the fast diffusion case
type: Item
instance of: scholarly article
title: Self-similar solutions of the \(p\)-Laplace heat equation: the fast diffusion case
zbMATH Open document ID: 1128.35058
published in: Pacific Journal of Mathematics
publication date: 2007-09-12T00:00:00Z
review text: This fundamental treatise contains a complete description of the self-similar solutions of the equation \(u_t-\text{div} (| \nabla u| ^p-2\nabla u)=0\) in the fast diffusion case (i.e. \(p\in (1, 2)\)). The list consists of signed solution of the form \(u(x,t)=(\pm t)^{-\alpha\setminus \beta w((\pm t)^{-1/\beta}| x| )} \) with \(\alpha\), \(\beta\) real, \(\beta\neq 0\), regular or singular at \(x=0\), and possibly not defined on all of \({\mathbb R}^N\times (0, \infty)\).
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 5190378
zbMATH Keywords: the \(p\)-Laplace heat equations
zbMATH Keywords: self-similar solutions
zbMATH Keywords: signed solution
author: Marie-Françoise Bidaut-Véron
reviewed by: Georgiĭ Anatol'evich Sviridyuk
MaRDI profile type: Publication
full work available at URL: pjm.2006.227.201
OpenAlex ID: W1980788937
DOI: 10.2140/PJM.2006.227.201
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description: scientific article; zbMATH DE number 5190378