We consider the Fokker-Planck equation with subcritical confinement force field which may not derive from a potential function. prove existence of unique positive equilibrium mass one and we establish some subgeometric, or geometric, rate convergence to multiple this (depending on space belongs initial datum) in many spaces. Our results generalize similar introduced by Toscani, Villani [33] Röc...

We prove that the solution of the Vlasov-Fokker-Planck equation converges to the unique stationary solution with same mass as time tends to infinity. The same result holds in the repulsive coulombic case for the Vlasov-Poisson-Fokker-Planck system; the newtonian attractive case is also studied. We establish positive and negative answers to the question of existence of a stationary solution for ...

This is the third paper in a series concerning the study of steady states of a Fokker-Planck equation in a general domain in R with Lp̄loc drift term and W 1,p̄ loc diffusion term for any p̄ > n. In this paper, we give some existence results of stationary measures of the Fokker-Planck equation under Lyapunov conditions which allow the degeneracy of diffusion.

We investigate a Smoluchowski equation (a nonlinear Fokker-Planck equation on the unit sphere), which arises in modeling of colloidal suspensions. We prove the dissipativity of the equation in 2D and 3D, in certain Gevrey classes of analytic functions.

We show how, beginning with the Fokker–Planck equation for electrons emitting synchrotron radiation in a storage ring, the corresponding equation for spin motion can be constructed. This is an equation of the Bloch type for the polarisation density.

We introduce a stochastic particle system that corresponds to the Fokker–Planck equation with decay in the many-particle limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an energy-dissipation functional in a Mosco-convergence sense. Moreover, we prove that the resulting functional, which involves entropic terms and the Wasserstein metric, is...