Entropy based moment closure for kinetic equations: Riemann problem and invariant regions

Entropy-based moment closure for kinetic equations: Riemann problem and invariant regions Jean-Franc¸ois Coulombel and Thierry Goudon CNRS & Universite Lille 1, Laboratoire Paul Painleve, UMR CNRS 8524 Cite scientifique, 59655 VILLENEUVE D'ASCQ Cedex, France and Team SIMPAF, INRIA Futurs E-mails: , November 8, 2005 Abstract We study a nonlinear hyperbolic system of balance laws that arises from an entropy- based moment closure of a kinetic equation. We show that the corresponding homogeneous Riemann problem can be solved without smallness assumption, and we exhibit invariant regions. AMS subject classification: 82C40, 35L60 35L67 1 Introduction This paper is devoted to the analysis of the following PDEs system ? ? ? ∂t?+ ∂xJ = 0 , ?2 ∂tJ + ∂x ( ?? (?J ? )) = ?J , (1) where the unknown are the density ?, and the current J , while ? is a positive scaling parameter. The function ? that appears in (1) is defined in the following way: ? : (?1,+1) ?? ]0,+∞[ u 7?? u2 + G? ( G?1(u) ) = F ?? F ( G?1(u) ) , (2) where we have let ?? ? R , F(?) := sinh(?)? , G(?) := coth(

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