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doi: 10.3934/krm.2022014
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## A moment closure based on a projection on the boundary of the realizability domain: Extension and analysis

 CMAP, École Polytechnique, CNRS UMR7641, Institut Polytechnique de Paris, Route de Saclay, Palaiseau, 91128, France

Received  January 2022 Revised  April 2022 Early access May 2022

Fund Project: The author is supported by DGA AID through MMEED project

A closure relation for moments equations in kinetic theory was recently introduced in [38], based on the study of the geometry of the set of moments. This relation was constructed from a projection of a moment vector toward the boundary of the set of moments and corresponds to approximating the underlying kinetic distribution as a sum of a chosen equilibrium distribution plus a sum of purely anisotropic Dirac distributions.

The present work generalizes this construction for kinetic equations involving unbounded velocities, i.e. to the Hamburger problem, and provides a deeper analysis of the resulting moment system. Especially, we provide representation results for moment vectors along the boundary of the moment set that implies the well-definition of the model. And the resulting moment model is shown to be weakly hyperbolic with peculiar properties of hyperbolicity and entropy of two subsystems, corresponding respectively to the equilibrium and to the purely anisotropic parts of the underlying kinetic distribution.

Citation: Teddy Pichard. A moment closure based on a projection on the boundary of the realizability domain: Extension and analysis. Kinetic and Related Models, doi: 10.3934/krm.2022014
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