Symmetry analysis of the two-dimensional diffusion equation with a source term
type: Item
instance of: scholarly article
title: Symmetry analysis of the two-dimensional diffusion equation with a source term
zbMATH Open document ID: 1160.35007
author: D. J. Arrigo
author: Luis R. Suazo
author: Olabode M. Sule
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-06-26T00:00:00Z
review text: The authors study the two-dimensional diffusion equation \(u_t=u_{xx}+u_{yy}+Q(u,u_x,u_y)\) where it is assumed that the source \(Q\) effectively depends on both derivatives. The main part of the paper consists of a lengthy calculation in which several classes of sources admitting non-trivial Lie point symmetries are identified (no complete classification is given). Then the authors proceed to non-classical symmetries, however only in the restricted form of Bluman-Cole. They show that this extension does not lead to different results in the considered cases.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 5167502
zbMATH Keywords: diffusion equation
zbMATH Keywords: nonlinear source
zbMATH Keywords: Lie symmetry
zbMATH Keywords: non-classical symmetry
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.12.027
OpenAlex ID: W2086956149
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DOI: 10.1016/J.JMAA.2006.12.027
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description: scientific article; zbMATH DE number 5167502