In this paper, we first show the uniqueness of invariant measures for the stochastic fast diffusion equation, which follows from an obtained new decay estimate. Then we establish the Harnack inequality for the stochastic fast diffusion equation with nonlinear perturbation in the drift and derive the heat kernel estimate and ultrabounded property for the associated transition semigroup. Moreover, the exponential ergodicity and the existence of a spectral gap are also investigated.
Corresponding Author(s):
LIU Wei,Email:wei.liu@uni-bielefeld.de
引用本文:
. Ergodicity of transition semigroups for stochastic fast diffusion equations[J]. Frontiers of Mathematics in China, 2011, 6(3): 449-472.
Wei LIU. Ergodicity of transition semigroups for stochastic fast diffusion equations. Front Math Chin, 2011, 6(3): 449-472.
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