[PDF][PDF] A review of mathematical topics in collisional kinetic theory

C Villani - Handbook of mathematical fluid dynamics, 2002‏ - cedricvillani.org
The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …

[ספר][B] Topics in optimal transportation

C Villani - 2021‏ - books.google.com
This is the first comprehensive introduction to the theory of mass transportation with its many—
and sometimes unexpected—applications. In a novel approach to the subject, the book both …

[ספר][B] Hypocoercivity

C Villani - 2009‏ - ams.org
This memoir attempts at a systematic study of convergence to stationary state for certain
classes of degenerate diffusive equations, taking the general form ${\frac {\partial f}{\partial …

On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations

A Arnold, P Markowich, G Toscani, A Unterreiter - 2001‏ - Taylor & Francis
It is well known that the analysis of the large-time asymptotics of Fokker-Planck type
equations by the entropy method is closely related to proving the validity of convex Sobolev …

On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation

L Desvillettes, C Villani - Inventiones mathematicae, 2005‏ - Springer
As part of our study of convergence to equilibrium for spatially inhomogeneous kinetic
equations, started in [21], we derive estimates on the rate of convergence to equilibrium for …

[ספר][B] Entropies and equilibria of many-particle systems: an essay on recent research

A Arnold, JA Carrillo, L Desvillettes, J Dolbeault… - 2004‏ - Springer
This essay is intended to present a fruitful collaboration which has developed among a
group of people whose names are listed above: entropy methods have proved over the last …

The Navier–Stokes limit of the Boltzmann equation for bounded collision kernels

F Golse, L Saint-Raymond - Inventiones mathematicae, 2004‏ - Springer
The present work establishes a Navier–Stokes limit for the Boltzmann equation considered
over the infinite spatial domain R 3. Appropriately scaled families of DiPerna-Lions …

On the spatially homogeneous landau equation for hard potentials part i: existence, uniqueness and smoothness

L Desvillettes, C Villani - Communications in Partial Differential …, 2000‏ - Taylor & Francis
We study the Cauchy problem for the homogeneous Landau equation of kinetic theory, in
the case of hard potentials. We prove that for a large class of initial data, there exists a …

On the trend to global equilibrium in spatially inhomogeneous entropy‐dissipating systems: The linear Fokker‐Planck equation

L Desvillettes, C Villani - … on Pure and Applied Mathematics: A …, 2001‏ - Wiley Online Library
We study the long‐time behavior of kinetic equations in which transport and spatial
confinement (in an exterior potential or in a box) are associated with a (degenerate) collision …

[PDF][PDF] On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis

PA Markowich, C Villani - Mat. Contemp, 2000‏ - cedricvillani.org
We present connections between the problem of trend to equilibrium for the Fokker-Planck
equation of statistical physics, and several inequalities from functional analysis, like …