Asymptotic behavior and hypercontractivity in nonautonomous   Ornstein-Uhlenbeck equations
  In this paper we investigate a class of nonautonomous linear parabolic problems with time depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic and non-periodic situation. Moreover, we show that the associated evolution operator is hypercontractive. 
Matthias Geissert, Alessandra Lunardi