Degond P., Pareschi L., Russo G. (eds.) Modeling and computational methods for kinetic equations

Springer Science, New York, 2004. – 359 pp.
The aim of this book is to provide a general overview of kinetic models and their applications to various contexts (gas dynamics, semiconductor modelling, granular flows, traffic flows, and so on.) Particular emphasis will be given to the derivation of the models and to the modem numerical methods available to obtain quantitative predictions from the models. The mathematical treatment, although rigorous, will be mostly maintained at a level accessible to a broad range of readers, including graduate students in applied sciences and engineers.Rarefied Gases.
Macroscopic limits of the Boltzmann equation: a review. - Pierre Degond.
Moment equations for charged particles: global existence results. - Giuseppe Ali, Angelo Marcello Anile.
Monte-Carlo methods for the Boltzmann equation. - Sergej Rjasanow.
Accurate numerical methods for the Boltzmann equation. - Francis Filbet, Giovanni Russo.
Finite-difference methods for the Boltzmann equation for binary gas mixtures. - Kazuo Aoki, Shingo Kosuge.
Applications.
Plasma kinetic models: the Fokker-Planck-Landau equation. - Laurent Desvillettes.
On multipole approximations of the Fokker-Planck-Landau operator. - Mohammed Lemou.
Traffic flow: models and numerics. - Axel Klar, Raimund Wegener.
Modelling and numerical methods for granular gases - Lorenzo Pareschi, GiuseppeToscani.
Quantum kinetic theory: modelling and numerics for Bose-Einstein condensation. - Weizhu Bao, Lorenzo Pareschi, Peter A. Markowich.
On coalescence equations and related models. - Philippe Laurencot, Stephane Mischler.