Hyperbolic to parabolic relaxation theory for quasilinear first order systems
type: Item
instance of: scholarly article
title: Hyperbolic to parabolic relaxation theory for quasilinear first order systems
zbMATH Open document ID: 0987.35103
author: Pierangelo Marcati
author: Bruno Rubino
published in: Journal of Differential Equations
publication date: 2000-08-07T00:00:00Z
review text: This paper is concerned with a quasilinear first-order system with a source term, and investigates the relaxation phenomena where the relaxed equilibria are described by means of an equation (or a system) of parabolic type. In particular a one-dimensional \(2\times 2\) system of genuinely nonlinear hyperbolic balance laws with a strong dissipative nonlinear term is analysed, and a different approach is used to study the limiting profiles in case of isentropic gas dynamics. The limiting profiles are given by the solutions of the convective linear parabolic equations, which include porous media type equation, and the convergence results are obtained. The paper may be of interest to someone working on conservation laws.
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 1454738
zbMATH Keywords: compressible Euler flow
zbMATH Keywords: strong dissipative nonlinear term
zbMATH Keywords: isentropic gas dynamics
zbMATH Keywords: limiting profiles
MaRDI profile type: Publication
full work available at URL: jdeq.1999.3676
OpenAlex ID: W1994170747
Wikidata QID: Q58619787
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DOI: 10.1006/JDEQ.1999.3676
description: scientific article; zbMATH DE number 1454738