Physics – Mathematical Physics
Scientific paper
2010-09-26
Physics
Mathematical Physics
35 pages, no figures. Version to appear on CPDE
Scientific paper
A class of linear kinetic Fokker-Planck equations with a non-trivial diffusion matrix and with periodic boundary conditions in the spatial variable is considered. After formulating the problem in a geometric setting, the question of the rate of convergence to equilibrium is studied within the formalism of differential calculus on Riemannian manifolds. Under explicit geometric assumptions on the velocity field, the energy function and the diffusion matrix, it is shown that global regular solutions converge in time to equilibrium with exponential rate. The result is proved by estimating the time derivative of a modified entropy functional, as recently proposed by Villani. For spatially homogeneous solutions the assumptions of the main theorem reduce to the curvature bound condition for the validity of logarithmic Sobolev inequalities discovered by Bakry and Emery. The result applies to the relativistic Fokker-Planck equation in the low temperature regime, for which exponential trend to equilibrium was previously unknown.
No associations
LandOfFree
Exponential convergence to equilibrium for kinetic Fokker-Planck equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Exponential convergence to equilibrium for kinetic Fokker-Planck equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exponential convergence to equilibrium for kinetic Fokker-Planck equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-561769