Affiliations: CNRS & Université Lille 1, Laboratoire Paul Painlevé, UMR CNRS 8524 Cité scientifique, 59655 Villeneuve d'Ascq cedex, France E-mails: {jfcoulom, thierry.goudon}@math.univ-lille1.fr | Laboratoire Jacques-Louis Lions, UMR CNRS 7598 Université Paris 7, 175 rue du Chevaleret, 75013 Paris, France E-mail: [email protected]
Abstract: It is a well-known fact that, in small mean free path regimes, kinetic equations can lead to diffusion equations. Besides, kinetic equations can be approached by a closed system of moments equations. In this paper, we are interested in a special closure based on an entropy minimization principle, as introduced earlier by Levermore. We investigate the behavior of the resulting nonlinear hyperbolic system in the diffusive scaling. We first establish various fundamental facts on this system, then we show that the hyperbolic system admits global smooth solutions, and is consistent with the diffusion limit. Similar features are also discussed for a simpler limited flux equation.
