Time-asymptotic behavior of wave propagation around a viscous shock profile
type: Item
instance of: scholarly article
title: Time-asymptotic behavior of wave propagation around a viscous shock profile
zbMATH Open document ID: 1190.35033
author: Tai-Ping Liu
author: Yanni Zeng
published in: Communications in Mathematical Physics
publication date: 2010-01-11T00:00:00Z
review text: The authors study the nonlinear stability of viscous shock waves for the system of viscous conservation laws \(u_t+f(u)_x=u_{xx}\). Using a new construction of a fundamental solution for a linearized system around a shock profile, they obtain, for the first time, a pointwise estimate of nonlinear wave interaction across a shock wave. Since these results apply to all ranges of weak shock waves and small perturbations, they reduce to the time-asymptotic behavior of a constant state perturbation, uniformly as the strength of the shock wave tends to zero.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 5655471
zbMATH Keywords: nonlinear stability
zbMATH Keywords: pointwise estimate
reviewed by: Evgeniy Panov
MaRDI profile type: Publication
full work available at URL: s00220-009-0820-6
OpenAlex ID: W1975684220
cites work: Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws
cites work: On a quasi-linear parabolic equation occurring in aerodynamics
cites work: Nonlinear asymptotic stability of viscous shock profiles for conservation laws
cites work: The partial differential equation ut + uux = μxx
cites work: Hyperbolic systems of conservation laws II
cites work: Nonlinear stability of shock waves for viscous conservation laws
cites work: Q4697952
cites work: Pointwise convergence to shock waves for viscous conservation laws
cites work: Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws
cites work: Compressible Navier-Stokes equations with zero heat conductivity
cites work: Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas
cites work: High-order essentially non-oscillatory scheme for viscoelasticity with fading memory
cites work: Q4314474
cites work: Nonlinear stability of viscous shock waves
cites work: L1 asymptotic behavior of compressible, isentropic, viscous 1‐D flow
cites work: \(L^ p\) asymptotic behavior of solutions to hyperbolic-parabolic systems of conservation laws
cites work: Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation
cites work: Gas flows with several thermal nonequilibrium modes
DOI: 10.1007/S00220-009-0820-6
description: scientific article; zbMATH DE number 5655471