Asymptotic behavior for scalar viscous conservation laws with boundary effect
type: Item
instance of: scholarly article
title: Asymptotic behavior for scalar viscous conservation laws with boundary effect
zbMATH Open document ID: 0871.35050
author: Tai-Ping Liu
author: Kenji Nishihara
published in: Journal of Differential Equations
publication date: 1997-05-28T00:00:00Z
review text: The authors consider the asymptotic stability for scalar viscous conservation laws \(u_t + f(u)_x = u_{xx}\) on the half-space \((-\infty, 0)\). The problem includes also boundary effects, the prescribed boundary values are \(u(-\infty) = u_-\) and \(u(0) = u_+\). The rigorous analysis is divided into three cases depending on the sign of the shock speed \(s\) of the shock \((u_-, u_+)\). For the case \(s\leq 0\) the form of asymptotic state of the solution is determined precisely and is related to the boundary layer of the solution at \(x=0\). For the case \(s < 0\) the stability of the solution is shown using weighted energy method. On the other hand for the case \(s=0\) only a conjecture on the form of asymptotic state can be presented. The case \(s>0\) is more simpler than the other cases and is treated also in the paper.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L67
zbMATH DE Number: 1000155
zbMATH Keywords: shock speed
zbMATH Keywords: asymptotic state of solution
MaRDI profile type: Publication
full work available at URL: jdeq.1996.3217
OpenAlex ID: W2074873995
DOI: 10.1006/JDEQ.1996.3217
description: scientific article; zbMATH DE number 1000155