### Trend to the equilibrium for kinetic Fokker-Planck equations on Riemannian manifolds

Calogero, S *(Granada)*

Friday 10 September 2010, 14:00-14:40

Seminar Room 1, Newton Institute

#### Abstract

In this talk I will present a result concerning the rate of convergence to the equilibrium for a class of degenerate transport-diffusive equations with periodic boundary conditions in the spatial variable. The diffusive part is given by the Laplace-Beltrami operator associated to a positive definite metric. Under suitable conditions on the velocity field and the Ricci curvature of the metric, all solutions convergence exponentially fast in time to the unique equilibrium state. The proof is by estimating the time derivative of the "modified" entropy in the formalism of Riemannian geometry.

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