Hypocoercive Diffusion Operators

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Hypocoercivity for kinetic equations with linear relaxation terms (2008, methodology): “Villani, see [10,11], and has been successfully applied to various models, see for instance [8].”
Spectral analysis of semigroups and growth-fragmentation equations (2013, background): “We refer the interested reader to [104] for a pedagogical introduction as well as to [56, 53, 88, 54, 55, 105, 29, 28] for some of the original articles.”
Couplings and quantitative contraction rates for Langevin dynamics (2017, background): “Several analytic approaches to convergence to equilibrium for kinetic Fokker-Planck equations have been proposed during the last 15 years [10, 17, 27, 25, 26, 40, 42, 11, 7, 33, 19, 20, 3].”
Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré (2007, background): “In studying fully degenerate cases, Villani introduces higher order functional inequalities (reminding the celebrated Γ2 criterion for logarithmic Sobolev inequality), see equation (11) in [29] and more generally [30].”
Large Time Asymptotics for Partially Dissipative Hyperbolic Systems (2011, methodology): “This kind of Lyapunov function is similar to those introduced by Villani [34] for the analysis of the decay of partially diffusive systems, and is also linked, as we mentioned above, to the extensive literature on damped wave equations (see [15,27], for instance).”