2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116350This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, by means of well-chosen Lyapunov functionals. Typical examples are the kinetic Fokker--Planck and Boltzmann equation. Many open problems and possible directions for future research are discussed.Analysis of PDEs35B40; 35K65; 76P05text