Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory

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Mathematical tools for kinetic equations (2004, background): “For large time behavior, we refer to [87] (part I), Desvillettes and Villani [44] for bounded domains, and to [101] for the whole space.”
Hypocoercivity (2006, background): “This last section is devoted to the Boltzmann equation; see [51] and the references therein for background and references on this model.”
Hypocoercive Diffusion Operators (2006, background): “A mathematically-oriented presentation of the Boltzmann equation can be found in my long review paper [27].”
Numerical methods for kinetic equations* (2014, methodology): “In this case, corresponding to α = −3, the Boltzmann integral diverges and the Landau equation can be derived in the grazing collision limit (Villani 2002).”