On the stability of viscous shock fronts for certain conservation laws in two-dimensional space
type: Item
instance of: scholarly article
title: On the stability of viscous shock fronts for certain conservation laws in two-dimensional space
zbMATH Open document ID: 0940.35132
author: Masataka Nishikawa
published in: Differential and Integral Equations
publication date: 2000-05-22T00:00:00Z
review text: The author investigates the Cauchy problem \[ u_t+f(u)_x=\mu \Delta u,\;u(0,x,y)=u_0(x,y),\^^M(t,x,y)\in \mathbb{R}^+\times \mathbb{R}^2, \] where the initial datum is asymptotically constant: \(u(x,y)\to u_\pm \) as \(x\to \pm \infty \) for any fixed \(y\). Local asymptotic stability of a (possibly shifted) travelling wave solution of the form \(u(t,x,y)=\phi (x-st)\) is proved provided that \(s,\;u_\pm \) satisfy the Rankine-Hugoniot condition and a generalized shock condition. Convexity of the flux is not required.
reviewed by: Hana Petzeltová
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 35L67
zbMATH DE Number: 1450177
zbMATH Keywords: planar shock front
zbMATH Keywords: viscous conservation law
zbMATH Keywords: Rankine-Hugoniot condition
zbMATH Keywords: generalized shock condition
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1450177