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Hyperbolic conservation laws with stiff relaxation terms and entropy
Author(s) -
Chen GuiQiang,
Levermore C. David,
Liu TaiPing
Publication year - 1994
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160470602
Subject(s) - conservation law , inviscid flow , mathematics , dissipative system , converse , nonlinear system , limiting , entropy (arrow of time) , mathematical analysis , convergence (economics) , classical mechanics , geometry , physics , thermodynamics , mechanical engineering , quantum mechanics , engineering , economics , economic growth
We study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms. Reduced systems, inviscid and viscous local conservation laws, and weakly nonlinear limits are derived through asymptotic expansions. An entropy condition is introduced for N × N systems that ensures the hyperbolicity of the reduced inviscid system. The resulting characteristic speeds are shown to be interlaced with those of the original system. Moreover, the first correction to the reduced system is shown to be dissipative. A partial converse is proved for 2 × 2 systems. This structure is then applied to study the convergence to the reduced dynamics for the 2 × 2 case. © 1994 John Wiley & Sons, Inc.