Transition to instability of planar viscous shock fronts: The refined stability condition
type: Item
instance of: scholarly article
title: Transition to instability of planar viscous shock fronts: The refined stability condition
zbMATH Open document ID: 1172.35060
DOI: 10.4171/ZAA/1361
author: Sylvie Benzoni-Gavage
author: Denis Serre
author: Kevin Zumbrun
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2008-11-27T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: In this paper, the authors develop a simplified perturbation formula for the viscosity coefficient \(\beta\) determined by the second derivatives of the Evans function associated with the linearized operator about the shock wave, which can be applied to general shock waves. It was showed by \textit{K. Zumbrun} and \textit{D. Serre} [Indiana Univ. Math. J. 48, No.~3, 937--992 (1999; Zbl 0944.76027)] that the viscosity coefficient \(\beta\) plays an important role for the transition under localized (\(L^1\cap H^s\)) perturbations.
reviewed by: Cheng He
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 37B20
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 5374717
zbMATH Keywords: Evens function
zbMATH Keywords: viscous conservation laws, spectral stability
zbMATH Keywords: shock wave
MaRDI profile type: Publication
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OpenAlex ID: W2093678083
description: scientific article; zbMATH DE number 5374717