Preprint 2003-003

An Entropy Condition and Global Existence Result for Hyperbolic Balance Laws

Wen-An Yong

Abstract: This paper presents a general result on the existence of global smooth solutions to hyperbolic systems of balance laws in several space variables. We propose an entropy condition and prove the existence of global smooth solutions for the systems with initial data close to constant equilibrium states where the entropy condition and Kawashima's condition are satisfied. In addition, we show that a system of balance laws satisfies Kawashima's condition if and only if so does its first-order approximation---a hyperbolic-parabolic system---derived from the Chapman-Enskog expansion. The result is applied to Bouchut's discrete velocity BGK models approximating hyperbolic systems of conservation laws.



Paper:
Available as PostScript (304 Kbytes) or gzipped PostScript (128 Kbytes; uncompress using gunzip).
Author(s):
Wen-An Yong, <yong.wen-an@iwr.uni-heidelberg.de>
Publishing information:
Preprint 02-34 (IWR/SFB 359), University of Heidelberg
Comments:
Submitted by:
<yong.wen-an@iwr.uni-heidelberg.de> January 5 2003.


[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <conservation@math.ntnu.no>
Last modified: Tue Jan 14 10:53:50 MET 2003