Structurally stable Riemann solutions
type: Item
instance of: scholarly article
title: Structurally stable Riemann solutions
zbMATH Open document ID: 0869.35062
author: Stephen Schecter
author: B. Plohr
author: Dan Marchesin
published in: Journal of Differential Equations
publication date: 1996-06-30T00:00:00Z
review text: This paper is the first in a series that studies Riemann problem for systems of two hyperbolic conservation laws. The analysis is grounded in the viscous profile (traveling wave) criterion for shocks, leading to consideration of the theory of bifurcation of vector fields. In this paper, the authors identify Riemann problems whose solutions are structurally stable. Such solutions can include transitional waves but not overcompressive shocks. The paper includes a description of how a transitional wave that is sonic (i.e., travels at characteristic speed) on both sides can arise in a structurally stable Riemann problem solution. As part of the systematic analysis the authors introduce a new index, the Riemann number, defined on individual waves. A Riemann problem solution is then shown to be structurally stable if the Riemann numbers across waves in the solution sum to two, and additional nondegeneracy conditions hold.
reviewed by: Michael Shearer
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L67
zbMATH DE Number: 880559
zbMATH Keywords: structural stability
zbMATH Keywords: transitional waves
zbMATH Keywords: overcompressive shocks
MaRDI profile type: Publication
OpenAlex ID: W2007585191
DOI: 10.1006/JDEQ.1996.0053
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description: scientific article; zbMATH DE number 880559