Theory of congruences and systems of conservation laws
type: Item
instance of: scholarly article
title: Theory of congruences and systems of conservation laws
zbMATH Open document ID: 1019.35062
DOI: 10.1007/BF02365075
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-10-20T00:00:00Z
review text: This paper focusses on new formulations of systems of conservation laws by using the geometrical language of the theory of congruence. The central part of the paper provides a correspondence between a system of conservation laws \[ u^i_t= (f^i({\mathbf u}))_x,\quad {\mathbf u}=(u^1,u^2,\dots ,u^n),\qquad i=1,\dots,n \] and an \(n\)-parameter family of straight lines in the \((n+1)\)-dimensional space with coordinates \(y^0,y^1,\dots,y^n\) defined by the equations \[ y^i=u^iy^0-f^i({\mathbf u}),\quad i=1,\cdots,n. \] The reciprocal transformations, the rarefaction curves, the shock adiabatic curves and the commuting property of systems of conservation laws are interpreted in the language of the theory of congruence. The Temple class of systems of conservation laws, especially with two components [\textit{B. Temple}, Trans. Am. Math. Soc. 280, 781-795 (1983; Zbl 0559.35046)], is analyzed in detail.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L67
zbMATH DE Number: 1348489
zbMATH Keywords: Temple class
zbMATH Keywords: reciprocal transformations
zbMATH Keywords: rarefaction curves
zbMATH Keywords: shock adiabatic curves
author: S. I. Agafonov
author: E. V. Ferapontov
reviewed by: Wen-Xiu Ma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1348489