Undercompressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity
type: Item
instance of: scholarly article
title: Undercompressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity
zbMATH Open document ID: 0930.35106
author: Matthew R. Schulze
author: Michael Shearer
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-04-27T00:00:00Z
full work available at URL: http://www.lib.ncsu.edu/resolver/1840.4/277
review text: The author discussed the Riemann problem for the hyperbolic system \[ u_t-v_x=0, \qquad v_t-\sigma (u)_x =0 \] with \(\sigma (u) = u^3 +u\), which is monotone but nonconvex. It is proved that for all jump initial data, taking constant in \(x>0\) and \(x<0\) respectively, the Riemann problem has a unique solution, which consist of rarefaction waves and admissible shock waves.
reviewed by: Shuxing Chen
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 1246319
zbMATH Keywords: Riemann problem
zbMATH Keywords: rarefaction waves
zbMATH Keywords: admissible shock waves
MaRDI profile type: Publication
OpenAlex ID: W2025411653
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DOI: 10.1006/JMAA.1998.6186
description: scientific article; zbMATH DE number 1246319