Basic structures of hyperbolic relaxation systems

Author: Yong Wen-An  

Publisher: Royal Society of Edinburgh

ISSN: 1473-7124

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.132, Iss.5, 2002-10, pp. : 1259-1274

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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.