Global actions of Lie symmetries for the nonlinear heat equation
type: Item
instance of: scholarly article
title: Global actions of Lie symmetries for the nonlinear heat equation
zbMATH Open document ID: 1179.35037
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-09-10T00:00:00Z
review text: Standard Lie symmetry theory of differential equations is mainly concerned with local Lie groups (or often even only with infinitesimal symmetries). Following an approach developed by \textit{M. Craddock} [J. Differ. Equations 116, No. 1, 202--247 (1995; Zbl 0845.35020), ibid. 166, No. 1, 107--131 (2000; Zbl 0962.35010)], the author shows how one can obtain for the nonlinear heat equation \(u_t=(k(u)u_x)_x\) a global action of the symmetry group by restricting to a class of smooth functions naturally arising via representation theory. Modulo equivalence transformations, one must consider four different cases of the function \(k(u)\). It turns out that in three of them a linear action arises; only for \(k(u)=e^u\) a nonlinear action is obtained.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 35B06
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 5602695
zbMATH Keywords: local Lie groups
zbMATH Keywords: infinitesimal symmetries
author: Mark R. Sepanski
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.06.047
OpenAlex ID: W2023825888
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DOI: 10.1016/J.JMAA.2009.06.047
description: scientific article; zbMATH DE number 5602695