Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types
type: Item
instance of: scholarly article
title: Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types
zbMATH Open document ID: 1078.35078
DOI: 10.1215/S0012-7094-04-12722-8
author: Daniela Lupo
author: Kevin R. Payne
published in: Duke Mathematical Journal
publication date: 2005-06-09T00:00:00Z
review text: For the Tricomi type equation \[ K(y) \Delta_x u + u_{yy} + f(u) = 0, \tag \(*\) \] where \((x,y)\in \mathbb R^N\times \mathbb R,\) \(N\geq 1,\) \(yK(y)>0,\) \(K(0)=0,\) the basic changes of basis of independent variables such as translation, rotation, dilation and inversion is considered. For these cases the conservation laws are founded. The uniqueness theorem for the Tricomi problem for equation \((*)\) in a star-like domain \(\Omega\) with \(N=2,\) \(f(u) = C u | u| ^{p},\) is proved with the help of symmetry groups.
Mathematics Subject Classification ID: 35M10
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 2174751
zbMATH Keywords: uniqueness
zbMATH Keywords: symmetry group
zbMATH Keywords: conservation law
zbMATH Keywords: Tricomi type equation
zbMATH Keywords: translation
zbMATH Keywords: rotation
zbMATH Keywords: dilation
zbMATH Keywords: inversion
zbMATH Keywords: symmetry groups
MaRDI profile type: Publication
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full work available at URL: s0012-7094-04-12722-8
OpenAlex ID: W2008063830
description: scientific article; zbMATH DE number 2174751