Simple waves and simple states in \(\mathbb{R}^2\)
type: Item
instance of: scholarly article
title: Simple waves and simple states in \(\mathbb{R}^2\)
zbMATH Open document ID: 0892.35110
author: J. Tabov
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-07-14T00:00:00Z
review text: The paper deals with systems (1) \(\sum_{i,j} a^i_{jk}(x,u) \partial u^j/\partial x^i = b_k(x,u)\), where \(x = (x^1,\dots,x^n)\), \(u = (u^1,\dots,u^m)\). Sought are solutions \(u^j = u^j(R)\) that can be written in terms of a single function \(R(x)\), \(j = 1,\dots,m\). The starting point is an equivalent overdetermined system formed by equations (1) and \(\text{det}(\partial u^j/\partial x^i) = 0\). A practical solving procedure is suggested, based on the investigation of resolving distributions of Pfaff systems. Details are provided in the case \(m = n = 2\).
Mathematics Subject Classification ID: 35N10
Mathematics Subject Classification ID: 58A17
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35F20
zbMATH DE Number: 1123610
zbMATH Keywords: Riemann invariant
zbMATH Keywords: resolving distribution
reviewed by: Michal Marvan
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5600
OpenAlex ID: W2049439456
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DOI: 10.1006/JMAA.1997.5600
description: scientific article; zbMATH DE number 1123610