Hypocoercivity of linear kinetic equations via Harris's Theorem

In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous

Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition based

Keywords: Hypocoercivity; linear kinetic equations; fat tail equilibrium; Fokker- Planck operator; anomalous diffusion; fractional diffusion limt; scattering oper- ator;

A key feature of our approach is that it clearly distinguishes the mechanisms of relaxation at microscopic level (convergence towards a local equilibrium, in velocity space)

A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit. Fractional diffusion limit for collisional kinetic equations:

Key words : kinetic Fokker-Planck equation, McKean-Vlasov equation, convergence to equilibrium, hypocoercivity, entropy, Wasserstein distance, logarithmic Sobolev inequality,

Desvillettes, Convergence to equilibrium in various situations for the solution of the Boltzmann equation, in Nonlinear Kinetic Theory and Mathematical Aspects of Hyperbolic

Keywords: stochastic differential equations, periodic solution, Markov process, Massera