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Basic structures of hyperbolic relaxation systems

Published online by Cambridge University Press:  12 July 2007

Wen-An Yong
Wen-An Yong
Affiliation:
IWR, Universitäat Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany (yong.wen-an@IWR.Uni-Heidelberg.De)
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Abstract

This work is concerned with basic structural properties of first-order hyperbolic systems with source terms divided by a small parameter ε. We identify a relaxation criterion necessary for the solution sequences indexed with ε to have reasonable limits as ε goes to zero. This relaxation criterion is shown to imply hyperbolicity of the reduced systems governing the limits. Moreover, we introduce a so-called GC-stability theory and strengthen the hyperbolicity result. The latter shows that there are no linearly stable hyperbolic relaxation approximations for non-hyperbolic conservation laws.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 5 , October 2002 , pp. 1259 - 1274
Copyright
Copyright © Royal Society of Edinburgh 2002

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