Long-time effect of relaxation for hyperbolic conservation laws
type: Item
instance of: scholarly article
title: Long-time effect of relaxation for hyperbolic conservation laws
zbMATH Open document ID: 0851.35086
DOI: 10.1007/BF02104510
published in: Communications in Mathematical Physics
publication date: 1996-05-13T00:00:00Z
review text: The author deals with a strictly hyperbolic system of conservation laws with relaxation of the form \[ u_t+ f(u, v)_x= 0,\quad v_t+ g(u, v)_x= h(u, v). \] Such equations appear in many physical systems. It is shown that the long-time effect of relaxation is equivalent to a viscous effect when the initial data is a perturbation of a constant equilibrium state. The corresponding solution tends to a diffusion wave time asymptotically. This diffusion wave carriers an invariant mass. The convergence rate to this diffusion in \(L^p\)-sense \((1\leq p\leq \infty)\) is also obtained and this rate is optimal.
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 878030
zbMATH Keywords: relaxation
zbMATH Keywords: diffusion wave
author: I-Liang Chern
reviewed by: Alexandr Doktor
MaRDI profile type: Publication
cites work: Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws
cites work: Convergence to diffusion waves of solutions for viscous conservation laws
cites work: Large-time behaviour of solutions to hyperbolic–parabolic systems of conservation laws and applications
cites work: Hyperbolic conservation laws with relaxation
cites work: Q5520417
cites work: Q4151274
full work available at URL: https://doi.org/10.1007/bf02104510
OpenAlex ID: W2027974963
description: scientific article; zbMATH DE number 878030