Discrete shocks for difference approximations to systems of conservation laws
type: Item
instance of: scholarly article
title: Discrete shocks for difference approximations to systems of conservation laws
zbMATH Open document ID: 0575.65087
DOI: 10.1016/0196-8858(84)90017-4
author: Daniel Michelson
published in: Advances in Applied Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The existence of planar weak discrete shocks for a wide class of difference approximations to systems of conservation laws is proved. The difference schemes have to be conservative, k-th order accurate, and, roughly speaking, \((k+1)-t\) order dissipative, where \(k=1\) or 3. The proof makes use of the central manifold theorem for an implicit map and of the fact that the stable and unstable manifolds of the differential flow \(y^{(k)}=y^ 2-1\) for \(k=3\) intersect transversally.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 3919708
zbMATH Keywords: conservative difference schemes
zbMATH Keywords: planar weak discrete shocks
zbMATH Keywords: dissipative
MaRDI profile type: Publication
full work available at URL: 0196-8858(84)90017-4
OpenAlex ID: W1965421536
cites work: On spectral analysis of non-monic matrix and operator polynomials. I: reduction to monic polynomials
cites work: Discrete shocks
cites work: Bifurcations and trajectories joining critical points
cites work: The entropy condition and the admissibility of shocks
cites work: Discrete shock profiles for systems of conservation laws
cites work: On fourth-order dissipation and single conservation laws
cites work: Stable viscosity matrices for systems of conservation laws
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description: scientific article; zbMATH DE number 3919708