Long time behavior of non-autonomous Fokker-Planck equations and the cooling of granular gases

Details Long time behavior of non-autonomous Fokker-Planck equations and the cooling of granular gases Long time behavior of non-autonomous Fokker-Planck equations and the cooling of granular gases

2004-10-05

arxiv.org/abs/cond-mat/0410108v1

Physics

Condensed Matter

Soft Condensed Matter

15 pages, submitted to Ukrainian Math. J

Scientific paper

We analyze the asymptotic behavior of linear Fokker-Planck equations with time-dependent coefficients. Relaxation towards a Maxwellian distribution with time-dependent temperature is shown under explicitly computable conditions. We apply this result to the study of Brownian motion in granular gases as introduced J. J. Brey, J. Dufty and A. Santos (1999), by showing that the Homogenous Cooling State attracts any solution at an algebraic rate.

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