Entropy and global existence for hyperbolic balance laws
type: Item
instance of: scholarly article
title: Entropy and global existence for hyperbolic balance laws
zbMATH Open document ID: 1058.35162
published in: Archive for Rational Mechanics and Analysis
publication date: 2004-11-05T00:00:00Z
review text: The paper is concerned with multidimensional systems of balance laws \[ U_t+\sum\limits_{j=1}^d F_j(U)_{x_j}=Q(U), \quad U=U(x,t), \quad (x,t)\in {\mathbb R}^d\times [0,+\infty). \] Under some structural conditions, including the entropy dissipation condition and the Kawashima condition, the author proves existence and stability of global smooth solutions with initial data close to a constant equilibrium state. It is also shown that the Kawashima condition reduces to the known Kawa\-shima condition for the hyperbolic-parabolic systems derived through the Chapman-Enskog expansion. Applications to Bouchut's discrete velocity BGK models are given.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 2113851
zbMATH Keywords: entropy dissipation condition
zbMATH Keywords: Kawashima condition
zbMATH Keywords: Chapman-Enskog expansion
zbMATH Keywords: Bouchut's discrete velocity BGK models
author: Wen-An Yong
reviewed by: Evgeniy Panov
MaRDI profile type: Publication
full work available at URL: s00205-003-0304-3
OpenAlex ID: W2005912733
DOI: 10.1007/S00205-003-0304-3
description: scientific article; zbMATH DE number 2113851