Preprint 1998-034

Construction of BGK Models with a Family of Kinetic Entropies for a Given System of Conservation Laws

François Bouchut

Abstract: We introduce a general framework for kinetic BGK models. We assume to be given a system of hyperbolic conservation laws with a family of Lax entropies, and we characterize the BGK models that lead to this system in the hydrodynamic limit, and that are compatible with the whole family of entropies. This is obtained by a new characterization of maxwellians as entropy minimizers, that can take into account the simultaneous minimization problems corresponding to the family of entropies. We deduce a general procedure to construct such BGK models, and we give examples and applications in gas dynamics.

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Construction of BGK models with a family of kinetic entropies for a given system of conservation laws.
François Bouchut , <>
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<> September 16 1998.

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