φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations
φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations
This paper is devoted to $ϕ$-entropies applied to Fokker-Planck and kinetic Fokker-Planck equations in the whole space, with confinement. The so-called $ϕ$-entropies are Lyapunov functionals which typically interpolate between Gibbs entropies and L2 estimates. We review some of their properties in the case of diffusion equations of Fokker-Planck type, give …