Strong viscous shocks for systems of conservation laws with a high order of dissipation
type: Item
instance of: scholarly article
title: Strong viscous shocks for systems of conservation laws with a high order of dissipation
zbMATH Open document ID: 0673.35074
DOI: 10.1016/0022-0396(88)90025-3
author: Daniel Michelson
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: The author considers viscous shock profiles for systems of conservation laws with an entropy function. These systems can be written in gradient- flux form \[ (f_ u(u))_ t+(g_ u(u))_ x=0, \] where f and g are scalar functions. Viscous profiles are travelling waves solutions of an associated parabolic system, that approximate shock waves and are determined as tajectories of an autonomous system of ordinary differential equations. Topological methods, in particular the Conley index, are applied to the associated system of ordinary differential equations. For such a treatment, there are various assumptions on the regularity and global behavior of the fluxes f and g.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 76D33
zbMATH DE Number: 4101743
zbMATH Keywords: viscous shock profiles
zbMATH Keywords: systems of conservation laws
zbMATH Keywords: entropy function
zbMATH Keywords: gradient-flux form
zbMATH Keywords: travelling waves
zbMATH Keywords: shock waves
zbMATH Keywords: tajectories
zbMATH Keywords: autonomous system of ordinary differential equations
zbMATH Keywords: Topological methods
zbMATH Keywords: Conley index
zbMATH Keywords: regularity
zbMATH Keywords: global behavior
reviewed by: Michael Shearer
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90025-3
OpenAlex ID: W2044931545
cites work: Q4180600
cites work: Q5329330
cites work: On the symmetric form of systems of conservation laws with entropy
cites work: Bifurcations and trajectories joining critical points
cites work: Q3213564
cites work: Discrete shocks for difference approximations to systems of conservation laws
cites work: A topological degree for orbits connecting critical points of autonomous systems
cites work: Stable Viscosities and Shock Profiles for Systems of Conservation Laws
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description: scientific article; zbMATH DE number 4101743