Long time behavior of nonautonomous Fokker-Planck equations and the cooling of granular gases.

Bertrand Lods (1) , Giuseppe Toscani (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 Dipartimento di matematica F. Casorati

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 by showing that the Homogenous Cooling State attracts any solution at an algebraic rate.

Domaines: Equations aux dérivées partielles [math.AP]

Bertrand Lods, Giuseppe Toscani. Long time behavior of nonautonomous Fokker-Planck equations and the cooling of granular gases.. Ukrainian Mathematical Journal, 2005, 57 (6), pp.923-935. ⟨10.1007/s11253-005-0240-5⟩. ⟨hal-00473905⟩