Exceptional symmetry reductions of Burgers' equation in two and three spatial dimensions
type: Item
instance of: scholarly article
title: Exceptional symmetry reductions of Burgers' equation in two and three spatial dimensions
zbMATH Open document ID: 0843.35099
DOI: 10.1007/BF00917446
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1996-08-15T00:00:00Z
review text: Die Burgersche Gleichung \[ {\partial u\over \partial t}= \nabla^2 u- u {\partial u\over \partial z} \] (\(D(u)= \text{const.}\), \(K(u)=\) Quadratfunktion) stellt einen wichtigen Spezialfall der nichtlinearen Gleichung von Richard \[ {\partial u\over \partial t}= \nabla(D(u) \nabla u)- {dK\over du} {\partial u\over \partial z} \] dar. Die Autoren zeigen, daß eine vollständige symmetrische Reduktion letzterer Gleichung auf eine gewöhnliche Differentialgleichung möglich ist. Sie bestimmen das optimale System der symmetrischen Operatoren, um die Erzeugung der minimalen vollständigen Reduktionsmenge zu ermöglichen. Auf diese Weise sind alle möglichen Reduktionen auf eine gewöhnliche Differentialgleichung bestimmt.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 798849
zbMATH Keywords: Burger's equation
zbMATH Keywords: Richard's equation
zbMATH Keywords: reduction
author: Maureen P. Edwards
author: Philip Broadbridge
reviewed by: Miloš Čanak
describes a project that uses: REDUCE
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00917446
OpenAlex ID: W2037411485
description: scientific article; zbMATH DE number 798849