Extended rotation and scaling groups for nonlinear diffusion equations
type: Item
instance of: scholarly article
title: Extended rotation and scaling groups for nonlinear diffusion equations
zbMATH Open document ID: 1160.35009
author: Huabing Jia
author: Wei Xu
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-08-22T00:00:00Z
review text: The essence of the paper is to consider solutions of various forms of the \((1+1)\)-dimensional nonlinear diffusion equation by means of the criterion of invariance under the action of some particular group. In each case a single differential equation containing several unknown functions is obtained. This is clained to be impossible to be solved and so various multitudinous special cases are presented in which it is possible to obtain a solution. Curiously the solutions tend to be quite simple and one wonders how the authors were able to concoct the often complex Ansätze to reach these solutions.
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 58J70
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 5315325
zbMATH Keywords: symmetry group
zbMATH Keywords: closed-form solution
reviewed by: P. G. L. Leach
MaRDI profile type: Publication
full work available at URL: j.na.2007.06.004
OpenAlex ID: W3149359678
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DOI: 10.1016/J.NA.2007.06.004
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description: scientific article; zbMATH DE number 5315325