The Evans function and stability criteria for degenerate viscous shock waves
type: Item
instance of: scholarly article
title: The Evans function and stability criteria for degenerate viscous shock waves
zbMATH Open document ID: 1058.35033
author: Peter Howard
author: Kevin Zumbrun
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-11-01T00:00:00Z
review text: The authors study stability of degenerate (or sonic) viscous shock waves for the system \[ u_t+f(u)_x=u_{xx}, \quad u,f\in {\mathbb R}^2. \] This problem reduces to the problem of spectrum stability for the linear operator found by linearizing the original system about the wave. To solve this problem the device of Evans functions is traditionally used. Results obtained through working with the Evans function have made critical use of some analiticity conditions. These conditions seem to fail in the case of degenerate waves. The authors surmount this obstacle by dividing the Evans function into two pieces: one analytic in a neighborhood of the origin, and one sufficiently small.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 2113138
zbMATH Keywords: spectrum stability
reviewed by: Evgeniy Panov
MaRDI profile type: Publication
full work available at URL: dcds.2004.10.837
OpenAlex ID: W1999091406
DOI: 10.3934/DCDS.2004.10.837
description: scientific article; zbMATH DE number 2113138